Dependent probabilities
Sometimes we deal with dependent events; as we may recall, from the chapter about the addition rule, everything becomes apparent with the example, so now we are going to do the same!
Example:
Imagine that we have 4 blue balls in the basket, 4 green balls, 2 red ones and 3 yellow balls.
Calculate the probability of pulling out when we pull out the blue ball first, followed by the green one, and finally the red.
Explanation:
When we get the blue ball, it will no longer be in the box; therefore, when we get the green one, there will be one less ball in our box, the same situation in the case of the red one.
At the moment when we get the blue ball, it will no longer be in the box; therefore, when we get the green one, there will be one less ball in our box, the same situation the case with the red one.
Such events are called dependent. The formula for calculating here is similar to the regular multiplication rule. Still, we should consider that when the first event comes, we calculate the probability for the second event given the fact that the first came.
Refer to the solution for our example to make everything clarified.
Solution:
Swipe to start coding
I consider that you figured out the ins and outs of probability. Now it's time to hone in on your skills a little bit!
In a card game, to win we have to get from the deck of cards first the ace, then the queen, then the nine. Calculate the probability of getting such a result.
- Calculate the probability to get the ace.
- Calculate the probability to get the queen.
- Calculate the probability to get the nine.
- Calculate the probability to win the game.
There are 52 cards in a deck, 4 of each.
Oplossing
Note
Try to experiment with the order of cards. Is the result vary?
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Sometimes we deal with dependent events; as we may recall, from the chapter about the addition rule, everything becomes apparent with the example, so now we are going to do the same!
Example:
Imagine that we have 4 blue balls in the basket, 4 green balls, 2 red ones and 3 yellow balls.
Calculate the probability of pulling out when we pull out the blue ball first, followed by the green one, and finally the red.
Explanation:
When we get the blue ball, it will no longer be in the box; therefore, when we get the green one, there will be one less ball in our box, the same situation in the case of the red one.
At the moment when we get the blue ball, it will no longer be in the box; therefore, when we get the green one, there will be one less ball in our box, the same situation the case with the red one.
Such events are called dependent. The formula for calculating here is similar to the regular multiplication rule. Still, we should consider that when the first event comes, we calculate the probability for the second event given the fact that the first came.
Refer to the solution for our example to make everything clarified.
Solution:
Swipe to start coding
I consider that you figured out the ins and outs of probability. Now it's time to hone in on your skills a little bit!
In a card game, to win we have to get from the deck of cards first the ace, then the queen, then the nine. Calculate the probability of getting such a result.
- Calculate the probability to get the ace.
- Calculate the probability to get the queen.
- Calculate the probability to get the nine.
- Calculate the probability to win the game.
There are 52 cards in a deck, 4 of each.
Oplossing
Note
Try to experiment with the order of cards. Is the result vary?
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Awesome!
Completion rate improved to 3.7single
