Probability & Statistics Quiz

1. Two events A and B represent drawing a red card or a face card from a standard deck of 52 cards. What is the probability of drawing a red card or a face card?

P(A \cup B) = P(A) + P(B) - P(A \cap B)

2. What this code will output?

3. Two fair dice are rolled. $A = \text{"first die is even"}$ , $B = \text{"sum of dice ≥ 10"}$ . What is $P(A ∩ B)$ ?

P(A \cap B) = P(A) \times P(B)

4. What this code will output?

5. In a deck: let $A = \text{"card is a King"}$ , $B = \text{"card is a face card"}$ . What is $P(A | B)$ ?

P(A|B) = \frac{P(A \cap B)}{P(B)}

6. What this code will output?

7. A bag has 5 red and 3 blue marbles. One marble is drawn and not replaced, then a second is drawn. What is $P(\text{second is red} | \text{first was blue})$ ?

P(A|B) = \frac{P(A \cap B)}{P(B)}

8. What this code will output?

9. A rare disease affects 0.5% of the population. Test sensitivity is 98% and false-positive rate is 3%. If a person tests positive, what is $P(\text{disease} | \text{positive})$ ?

P(D|Pos) = \frac{P(Pos|D)P(D)}{P(Pos)}

10. What this code will output?

11. Which statement is true about a sample and population (and the sample mean)?

\bar{x} = \frac{1}{n}\sum^n_{i=1}x_i

12. What this code will output?

13. If 12 successes are observed in a sample of 50, what is the sample proportion $\hat{p}$ ?

\hat{p} = \frac{x}{n}

14. What this code will output?

15. Which sampling method is most likely to introduce bias in a survey about average weekly exercise time?

\bar{x} = \frac{1}{n}\sum^n_{i=1}x_i

16. What this code will output?

17. If every data point in a dataset is increased by constant c, which measure(s) change?

\mu = \frac{\sum{x_i}}{N}

18. What this code will output?

19. Population variance formula and compute variance for [2,4,6,8].

\sigma^2 = \frac{\sum(x_i - \mu)^2}{N}

20. What this code will output?

21. Binomial probability formula. For n=10, p=0.5, what is P(X=3)?

P(X=k)=\begin{pmatrix}n\\k\end{pmatrix}p^k(1-p)^{n-k}

22. What this code will output?

23. Z-score formula: for $\mathcal{N}(μ=100, σ=15)$ , what is z for $x=130$ ?

z = \frac{x-\mu}{\sigma}

24. What this code will output?

25. $\text{Uniform}(0,10)$ . What is $P(2 ≤ X ≤ 5)$ ?

f(x) = \frac{1}{b-a},\quad for\ a \le x \le b

26. What this code will output?

Two events A and B represent drawing a red card or a face card from a standard deck of 52 cards. What is the probability of drawing a red card or a face card?

P(A \cup B) = P(A) + P(B) - P(A \cap B)

Select the correct answer

0.58

0.60

0.62

0.64

What this code will output?

Select the correct answer

0.65

0.75

0.85

0.90

Two fair dice are rolled. $A = \text{"first die is even"}$ , $B = \text{"sum of dice ≥ 10"}$ . What is $P(A ∩ B)$ ?

P(A \cap B) = P(A) \times P(B)

Select the correct answer

\frac{1}{6}

\frac{1}{3}

\frac{1}{2}

\frac{2}{3}

What this code will output?

Select the correct answer

0.20

0.22

0.24

0.26

In a deck: let $A = \text{"card is a King"}$ , $B = \text{"card is a face card"}$ . What is $P(A | B)$ ?

P(A|B) = \frac{P(A \cap B)}{P(B)}

Select the correct answer

0.25

0.33

0.50

0.75

What this code will output?

Select the correct answer

0.28

0.30

0.32

0.35

A bag has 5 red and 3 blue marbles. One marble is drawn and not replaced, then a second is drawn. What is $P(\text{second is red} | \text{first was blue})$ ?

P(A|B) = \frac{P(A \cap B)}{P(B)}

Select the correct answer

\frac{5}{9}

\frac{4}{9}

\frac{3}{8}

\frac{5}{7}

What this code will output?

Select the correct answer

0.57

0.58

0.59

0.60

A rare disease affects 0.5% of the population. Test sensitivity is 98% and false-positive rate is 3%. If a person tests positive, what is $P(\text{disease} | \text{positive})$ ?

P(D|Pos) = \frac{P(Pos|D)P(D)}{P(Pos)}

Select the correct answer

0.12

0.16

0.18

0.14

What this code will output?

Select the correct answer

0.60

0.62

0.63

0.64

Which statement is true about a sample and population (and the sample mean)?

\bar{x} = \frac{1}{n}\sum^n_{i=1}x_i

Select the correct answer

The population mean is always computed from the sample and equals the sample mean.

The sample mean is a statistic that estimates the population mean and can vary between different samples.

Population mean must be larger than sample mean.

The sample mean always equals the median.

What this code will output?

Select the correct answer

7.40

8.40

9.20

10.00

If 12 successes are observed in a sample of 50, what is the sample proportion $\hat{p}$ ?

\hat{p} = \frac{x}{n}

Select the correct answer

0.20

0.30

0.26

0.24

What this code will output?

Select the correct answer

0.22

0.23

0.25

0.24

Which sampling method is most likely to introduce bias in a survey about average weekly exercise time?

\bar{x} = \frac{1}{n}\sum^n_{i=1}x_i

Select the correct answer

Simple random sampling from the entire city.

Stratified random sampling by age groups.

Convenience sampling at a local gym.

Systematic sampling from a city roster with random start.

What this code will output?

Select the correct answer

48.13

49.13

50.00

51.25

If every data point in a dataset is increased by constant c, which measure(s) change?

\mu = \frac{\sum{x_i}}{N}

Select the correct answer

Mean only

Variance only

Standard deviation only

Variance and mean

What this code will output?

Select the correct answer

12.0

13.0

14.0

15.0

Population variance formula and compute variance for [2,4,6,8].

\sigma^2 = \frac{\sum(x_i - \mu)^2}{N}

Select the correct answer

What this code will output?

Select the correct answer

4.00

5.00

6.00

7.00

Binomial probability formula. For n=10, p=0.5, what is P(X=3)?

P(X=k)=\begin{pmatrix}n\\k\end{pmatrix}p^k(1-p)^{n-k}

Select the correct answer

0.08

0.12

0.15

0.20

What this code will output?

Select the correct answer

0.200

0.250

0.296

0.350

Z-score formula: for $\mathcal{N}(μ=100, σ=15)$ , what is z for $x=130$ ?

z = \frac{x-\mu}{\sigma}

Select the correct answer

1.5

2.0

2.5

3.0

What this code will output?

Select the correct answer

0.50

0.68

0.95

0.99

$\text{Uniform}(0,10)$ . What is $P(2 ≤ X ≤ 5)$ ?

f(x) = \frac{1}{b-a},\quad for\ a \le x \le b

Select the correct answer

0.20

0.50

0.40

0.30

What this code will output?

Select the correct answer

0.18

0.22

0.20

0.25

War alles klar?

Wie können wir es verbessern?

Danke für Ihr Feedback!

Abschnitt 5. Kapitel 13

Fragen Sie AI

Fragen Sie alles oder probieren Sie eine der vorgeschlagenen Fragen, um unser Gespräch zu beginnen

Suggested prompts:

Can you explain this in simpler terms?

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Can you give me a real-world example?

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Probability & Statistics Quiz

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1. Two events A and B represent drawing a red card or a face card from a standard deck of 52 cards. What is the probability of drawing a red card or a face card?

P(A \cup B) = P(A) + P(B) - P(A \cap B)

2. What this code will output?

3. Two fair dice are rolled. $A = \text{"first die is even"}$ , $B = \text{"sum of dice ≥ 10"}$ . What is $P(A ∩ B)$ ?

P(A \cap B) = P(A) \times P(B)

4. What this code will output?

5. In a deck: let $A = \text{"card is a King"}$ , $B = \text{"card is a face card"}$ . What is $P(A | B)$ ?

P(A|B) = \frac{P(A \cap B)}{P(B)}

6. What this code will output?

7. A bag has 5 red and 3 blue marbles. One marble is drawn and not replaced, then a second is drawn. What is $P(\text{second is red} | \text{first was blue})$ ?

P(A|B) = \frac{P(A \cap B)}{P(B)}

8. What this code will output?

9. A rare disease affects 0.5% of the population. Test sensitivity is 98% and false-positive rate is 3%. If a person tests positive, what is $P(\text{disease} | \text{positive})$ ?

P(D|Pos) = \frac{P(Pos|D)P(D)}{P(Pos)}

10. What this code will output?

11. Which statement is true about a sample and population (and the sample mean)?

\bar{x} = \frac{1}{n}\sum^n_{i=1}x_i

12. What this code will output?

13. If 12 successes are observed in a sample of 50, what is the sample proportion $\hat{p}$ ?

\hat{p} = \frac{x}{n}

14. What this code will output?

15. Which sampling method is most likely to introduce bias in a survey about average weekly exercise time?

\bar{x} = \frac{1}{n}\sum^n_{i=1}x_i

16. What this code will output?

17. If every data point in a dataset is increased by constant c, which measure(s) change?

\mu = \frac{\sum{x_i}}{N}

18. What this code will output?

19. Population variance formula and compute variance for [2,4,6,8].

\sigma^2 = \frac{\sum(x_i - \mu)^2}{N}

20. What this code will output?

21. Binomial probability formula. For n=10, p=0.5, what is P(X=3)?

P(X=k)=\begin{pmatrix}n\\k\end{pmatrix}p^k(1-p)^{n-k}

22. What this code will output?

23. Z-score formula: for $\mathcal{N}(μ=100, σ=15)$ , what is z for $x=130$ ?

z = \frac{x-\mu}{\sigma}

24. What this code will output?

25. $\text{Uniform}(0,10)$ . What is $P(2 ≤ X ≤ 5)$ ?

f(x) = \frac{1}{b-a},\quad for\ a \le x \le b

26. What this code will output?

Two events A and B represent drawing a red card or a face card from a standard deck of 52 cards. What is the probability of drawing a red card or a face card?

P(A \cup B) = P(A) + P(B) - P(A \cap B)

Select the correct answer

0.58

0.60

0.62

0.64

What this code will output?

Select the correct answer

0.65

0.75

0.85

0.90

Two fair dice are rolled. $A = \text{"first die is even"}$ , $B = \text{"sum of dice ≥ 10"}$ . What is $P(A ∩ B)$ ?

P(A \cap B) = P(A) \times P(B)

Select the correct answer

\frac{1}{6}

\frac{1}{3}

\frac{1}{2}

\frac{2}{3}

What this code will output?

Select the correct answer

0.20

0.22

0.24

0.26

In a deck: let $A = \text{"card is a King"}$ , $B = \text{"card is a face card"}$ . What is $P(A | B)$ ?

P(A|B) = \frac{P(A \cap B)}{P(B)}

Select the correct answer

0.25

0.33

0.50

0.75

What this code will output?

Select the correct answer

0.28

0.30

0.32

0.35

A bag has 5 red and 3 blue marbles. One marble is drawn and not replaced, then a second is drawn. What is $P(\text{second is red} | \text{first was blue})$ ?

P(A|B) = \frac{P(A \cap B)}{P(B)}

Select the correct answer

\frac{5}{9}

\frac{4}{9}

\frac{3}{8}

\frac{5}{7}

What this code will output?

Select the correct answer

0.57

0.58

0.59

0.60

A rare disease affects 0.5% of the population. Test sensitivity is 98% and false-positive rate is 3%. If a person tests positive, what is $P(\text{disease} | \text{positive})$ ?

P(D|Pos) = \frac{P(Pos|D)P(D)}{P(Pos)}

Select the correct answer

0.12

0.16

0.18

0.14

What this code will output?

Select the correct answer

0.60

0.62

0.63

0.64

Which statement is true about a sample and population (and the sample mean)?

\bar{x} = \frac{1}{n}\sum^n_{i=1}x_i

Select the correct answer

The population mean is always computed from the sample and equals the sample mean.

The sample mean is a statistic that estimates the population mean and can vary between different samples.

Population mean must be larger than sample mean.

The sample mean always equals the median.

What this code will output?

Select the correct answer

7.40

8.40

9.20

10.00

If 12 successes are observed in a sample of 50, what is the sample proportion $\hat{p}$ ?

\hat{p} = \frac{x}{n}

Select the correct answer

0.20

0.30

0.26

0.24

What this code will output?

Select the correct answer

0.22

0.23

0.25

0.24

Which sampling method is most likely to introduce bias in a survey about average weekly exercise time?

\bar{x} = \frac{1}{n}\sum^n_{i=1}x_i

Select the correct answer

Simple random sampling from the entire city.

Stratified random sampling by age groups.

Convenience sampling at a local gym.

Systematic sampling from a city roster with random start.

What this code will output?

Select the correct answer

48.13

49.13

50.00

51.25

If every data point in a dataset is increased by constant c, which measure(s) change?

\mu = \frac{\sum{x_i}}{N}

Select the correct answer

Mean only

Variance only

Standard deviation only

Variance and mean

What this code will output?

Select the correct answer

12.0

13.0

14.0

15.0

Population variance formula and compute variance for [2,4,6,8].

\sigma^2 = \frac{\sum(x_i - \mu)^2}{N}

Select the correct answer

What this code will output?

Select the correct answer

4.00

5.00

6.00

7.00

Binomial probability formula. For n=10, p=0.5, what is P(X=3)?

P(X=k)=\begin{pmatrix}n\\k\end{pmatrix}p^k(1-p)^{n-k}

Select the correct answer

0.08

0.12

0.15

0.20

What this code will output?

Select the correct answer

0.200

0.250

0.296

0.350

Z-score formula: for $\mathcal{N}(μ=100, σ=15)$ , what is z for $x=130$ ?

z = \frac{x-\mu}{\sigma}

Select the correct answer

1.5

2.0

2.5

3.0

What this code will output?

Select the correct answer

0.50

0.68

0.95

0.99

$\text{Uniform}(0,10)$ . What is $P(2 ≤ X ≤ 5)$ ?

f(x) = \frac{1}{b-a},\quad for\ a \le x \le b

Select the correct answer

0.20

0.50

0.40

0.30

What this code will output?

Select the correct answer

0.18

0.22

0.20

0.25

War alles klar?

Wie können wir es verbessern?

Danke für Ihr Feedback!

Abschnitt 5. Kapitel 13

Probability & Statistics Quiz

1. Two events A and B represent drawing a red card or a face card from a standard deck of 52 cards. What is the probability of drawing a red card or a face card?

2. What this code will output?

3. Two fair dice are rolled. A="first die is even"A = \text{"first die is even"}A="first die is even", B="sum of dice ≥ 10"B = \text{"sum of dice ≥ 10"}B="sum of dice ≥ 10". What is P(A∩B)P(A ∩ B)P(A∩B)?

4. What this code will output?

5. In a deck: let A="card is a King"A = \text{"card is a King"}A="card is a King", B="card is a face card"B = \text{"card is a face card"}B="card is a face card". What is P(A∣B)P(A | B)P(A∣B)?

6. What this code will output?

7. A bag has 5 red and 3 blue marbles. One marble is drawn and not replaced, then a second is drawn. What is P(second is red∣first was blue)P(\text{second is red} | \text{first was blue})P(second is red∣first was blue)?

8. What this code will output?

9. A rare disease affects 0.5% of the population. Test sensitivity is 98% and false-positive rate is 3%. If a person tests positive, what is P(disease∣positive)P(\text{disease} | \text{positive})P(disease∣positive)?

10. What this code will output?

11. Which statement is true about a sample and population (and the sample mean)?

12. What this code will output?

13. If 12 successes are observed in a sample of 50, what is the sample proportion p^\hat{p}p^​?

14. What this code will output?

15. Which sampling method is most likely to introduce bias in a survey about average weekly exercise time?

16. What this code will output?

17. If every data point in a dataset is increased by constant c, which measure(s) change?

18. What this code will output?

19. Population variance formula and compute variance for [2,4,6,8].

20. What this code will output?

21. Binomial probability formula. For n=10, p=0.5, what is P(X=3)?

22. What this code will output?

23. Z-score formula: for N(μ=100,σ=15)\mathcal{N}(μ=100, σ=15)N(μ=100,σ=15), what is z for x=130x=130x=130?

24. What this code will output?

25. Uniform(0,10)\text{Uniform}(0,10)Uniform(0,10). What is P(2≤X≤5)P(2 ≤ X ≤ 5)P(2≤X≤5)?

26. What this code will output?

Awesome!

Probability & Statistics Quiz

1. Two events A and B represent drawing a red card or a face card from a standard deck of 52 cards. What is the probability of drawing a red card or a face card?

2. What this code will output?

3. Two fair dice are rolled. A="first die is even"A = \text{"first die is even"}A="first die is even", B="sum of dice ≥ 10"B = \text{"sum of dice ≥ 10"}B="sum of dice ≥ 10". What is P(A∩B)P(A ∩ B)P(A∩B)?

4. What this code will output?

5. In a deck: let A="card is a King"A = \text{"card is a King"}A="card is a King", B="card is a face card"B = \text{"card is a face card"}B="card is a face card". What is P(A∣B)P(A | B)P(A∣B)?

6. What this code will output?

7. A bag has 5 red and 3 blue marbles. One marble is drawn and not replaced, then a second is drawn. What is P(second is red∣first was blue)P(\text{second is red} | \text{first was blue})P(second is red∣first was blue)?

8. What this code will output?

9. A rare disease affects 0.5% of the population. Test sensitivity is 98% and false-positive rate is 3%. If a person tests positive, what is P(disease∣positive)P(\text{disease} | \text{positive})P(disease∣positive)?

10. What this code will output?

11. Which statement is true about a sample and population (and the sample mean)?

12. What this code will output?

13. If 12 successes are observed in a sample of 50, what is the sample proportion p^\hat{p}p^​?

14. What this code will output?

15. Which sampling method is most likely to introduce bias in a survey about average weekly exercise time?

16. What this code will output?

17. If every data point in a dataset is increased by constant c, which measure(s) change?

18. What this code will output?

19. Population variance formula and compute variance for [2,4,6,8].

20. What this code will output?

21. Binomial probability formula. For n=10, p=0.5, what is P(X=3)?

22. What this code will output?

23. Z-score formula: for N(μ=100,σ=15)\mathcal{N}(μ=100, σ=15)N(μ=100,σ=15), what is z for x=130x=130x=130?

24. What this code will output?

25. Uniform(0,10)\text{Uniform}(0,10)Uniform(0,10). What is P(2≤X≤5)P(2 ≤ X ≤ 5)P(2≤X≤5)?

26. What this code will output?

3. Two fair dice are rolled. $A = \text{"first die is even"}$ , $B = \text{"sum of dice ≥ 10"}$ . What is $P(A ∩ B)$ ?

5. In a deck: let $A = \text{"card is a King"}$ , $B = \text{"card is a face card"}$ . What is $P(A | B)$ ?

7. A bag has 5 red and 3 blue marbles. One marble is drawn and not replaced, then a second is drawn. What is $P(\text{second is red} | \text{first was blue})$ ?

9. A rare disease affects 0.5% of the population. Test sensitivity is 98% and false-positive rate is 3%. If a person tests positive, what is $P(\text{disease} | \text{positive})$ ?

13. If 12 successes are observed in a sample of 50, what is the sample proportion $\hat{p}$ ?

23. Z-score formula: for $\mathcal{N}(μ=100, σ=15)$ , what is z for $x=130$ ?

25. $\text{Uniform}(0,10)$ . What is $P(2 ≤ X ≤ 5)$ ?

3. Two fair dice are rolled. $A = \text{"first die is even"}$ , $B = \text{"sum of dice ≥ 10"}$ . What is $P(A ∩ B)$ ?

5. In a deck: let $A = \text{"card is a King"}$ , $B = \text{"card is a face card"}$ . What is $P(A | B)$ ?

7. A bag has 5 red and 3 blue marbles. One marble is drawn and not replaced, then a second is drawn. What is $P(\text{second is red} | \text{first was blue})$ ?

9. A rare disease affects 0.5% of the population. Test sensitivity is 98% and false-positive rate is 3%. If a person tests positive, what is $P(\text{disease} | \text{positive})$ ?

13. If 12 successes are observed in a sample of 50, what is the sample proportion $\hat{p}$ ?

23. Z-score formula: for $\mathcal{N}(μ=100, σ=15)$ , what is z for $x=130$ ?

25. $\text{Uniform}(0,10)$ . What is $P(2 ≤ X ≤ 5)$ ?