Course Content

Probability Theory

1. Learn Basic Rules

Random Variable Bernoulli Trial 1/2 Bernoulli Trial 2/2 Binomial Probability 1/2 Binomial probability 2/2

2. Probabilities of Several Events

Add Probabilities Calculate Connected Probabilities Challenge Multiply probabilities Dependent probabilities Law of Total Probability Bayes Theorem Challenge

3. Conducting Fascinating Experiments

The First Experiment The Second Experiment The Third Experiment Combine Your Knowledge

4. Discrete Distributions

Discrete Uniform Distribution Calculate Fascinating Probability Bernoulli Distribution Binomial Distribution Challenge Poisson Distribution Challenge

5. Normal Distribution

Normal Distribution Challenge 1 Сhallenge 2

The Second Experiment

As we remember from the previous chapter, it was almost impossible to figure out the probability of getting exactly 1000 positive responses among 20 000 answers, with the probability of 20% of getting a positive answer. But let's simplify it a little bit by changing the first part of the task. Here, we should calculate the probability of getting 1000 or more positive answers.

General formula:

In this experiment, we will work with the binom.sf(k, n, p) function. This function helps calculate the probability of receiving k or more successes among n trials with the probability of success for each experiment p.

Example:


              1234
            
from scipy.stats import binom
# Calculate the probability
experiment = binom.sf(k = 1000, n = 20000, p=0.20)
print(experiment)

Explanation:

from scipy.stats import binom importing object from scipy.stats.
binom.sf(k = 1000, n = 20000, p=0.20) the probability of getting more than 1000(inclusive) successes amoung 20 000 trials with the probability of success 20 %

Interesting fact:

As we remember in the previous chapter, we received 0%, but here the probability is 1.0 or 100%. In this case, the enormous sample was for us; further, compare this output with the output in the task, where the sample is significantly less.

Task

Here, we should cope with almost the same task as in the previous chapter, but a little bit changed.

Your task here is to calculate the probability that 5 or more kittens will find a home, there are 12 kittens in the shelter. In this city, kittens are taken from a shelter with a probability of 75%. Import relevant library to do it.

The output here is going to be less hopeful.

The probability of that exactly 5 kittens will be taken is 0.011471271514892587.

Import binom object from scipy.stats.
Calculate the probability that '5' or more kittens of 12 will find home with the probability of success 75%.

The output here is going to be less hopeful.

Note
As we may recognize, in both cases the probability increased from the previous chapter to this one. By the way, our result will be less if we want to calculate a defined number of successes, try to allow our experiment to have an error.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Everything was clear?

Thanks for your feedback!

Section 3. Chapter 2

The Second Experiment

General formula:

Example:


              1234
            
from scipy.stats import binom
# Calculate the probability
experiment = binom.sf(k = 1000, n = 20000, p=0.20)
print(experiment)

Explanation:

from scipy.stats import binom importing object from scipy.stats.
binom.sf(k = 1000, n = 20000, p=0.20) the probability of getting more than 1000(inclusive) successes amoung 20 000 trials with the probability of success 20 %

Interesting fact:

Task

Here, we should cope with almost the same task as in the previous chapter, but a little bit changed.

The output here is going to be less hopeful.

The probability of that exactly 5 kittens will be taken is 0.011471271514892587.

Import binom object from scipy.stats.
Calculate the probability that '5' or more kittens of 12 will find home with the probability of success 75%.

The output here is going to be less hopeful.

Note
As we may recognize, in both cases the probability increased from the previous chapter to this one. By the way, our result will be less if we want to calculate a defined number of successes, try to allow our experiment to have an error.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Everything was clear?

Thanks for your feedback!

Section 3. Chapter 2

The Second Experiment

General formula:

Example:


              1234
            
from scipy.stats import binom
# Calculate the probability
experiment = binom.sf(k = 1000, n = 20000, p=0.20)
print(experiment)

Explanation:

from scipy.stats import binom importing object from scipy.stats.
binom.sf(k = 1000, n = 20000, p=0.20) the probability of getting more than 1000(inclusive) successes amoung 20 000 trials with the probability of success 20 %

Interesting fact:

Task

Here, we should cope with almost the same task as in the previous chapter, but a little bit changed.

The output here is going to be less hopeful.

The probability of that exactly 5 kittens will be taken is 0.011471271514892587.

Import binom object from scipy.stats.
Calculate the probability that '5' or more kittens of 12 will find home with the probability of success 75%.

The output here is going to be less hopeful.

Note
As we may recognize, in both cases the probability increased from the previous chapter to this one. By the way, our result will be less if we want to calculate a defined number of successes, try to allow our experiment to have an error.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Everything was clear?

Thanks for your feedback!

General formula:

Example:


              1234
            
from scipy.stats import binom
# Calculate the probability
experiment = binom.sf(k = 1000, n = 20000, p=0.20)
print(experiment)

Explanation:

from scipy.stats import binom importing object from scipy.stats.
binom.sf(k = 1000, n = 20000, p=0.20) the probability of getting more than 1000(inclusive) successes amoung 20 000 trials with the probability of success 20 %

Interesting fact:

Task

Here, we should cope with almost the same task as in the previous chapter, but a little bit changed.

The output here is going to be less hopeful.

The probability of that exactly 5 kittens will be taken is 0.011471271514892587.

Import binom object from scipy.stats.
Calculate the probability that '5' or more kittens of 12 will find home with the probability of success 75%.

The output here is going to be less hopeful.

Note
As we may recognize, in both cases the probability increased from the previous chapter to this one. By the way, our result will be less if we want to calculate a defined number of successes, try to allow our experiment to have an error.

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Section 3. Chapter 2

Switch to desktop for real-world practiceContinue from where you are using one of the options below