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Conditional Probability




In these lessons, we will learn what is conditional probability and how to use the formula for conditional probability.

Related Topics: More Lessons on Probability

What is Conditional Probability?
The probability of an event occurring given that another event has already occurred is called a conditional probability.

Recall that when two events, A and B, are dependent, the probability of both occurring is

P(A and B) = P(A) × P(B given A)
or P(A and B) = P(A) × P(B | A)

If we divide both sides of the equation by P(A) we get the
Formula for Conditional Probability

Formula for Conditional Probability

How to find the Conditional Probability from a word problem?
Step 1: Write out the Conditional Probability Formula in terms of the problem
Step 2: Substitute in the values and solve

Example:

Susan took two tests. The probability of her passing both tests is 0.6. The probability of her passing the first test is 0.8. What is the probability of her passing the second test given that she has passed the first test?

Solution:




Example:

A bag contains red and blue marbles. Two marbles are drawn without replacement. The probability of selecting a red marble and then a blue marble is 0.28. The probability of selecting a red marble on the first draw is 0.5. What is the probability of selecting a blue marble on the second draw, given that the first marble drawn was red?

Solution:

conditional-probability

Example:

What is the probability that the total of two dice will be greater than 9, given that the first die is a 5?

Solution:

Let A = first die is 5

Let B = total of two dice is greater than 9

P(A) =

Possible outcomes for A and B: (5, 5), (5, 6)

P(A and B) =



 

Videos

Conditional Probability
This video gives an introduction of conditional probability.
Conditional probability is about narrowing down the set of possible circumstances so that the statistics can be measured more accurately.
Conditional Probability: Basic Definition
This video introduces the basic definition of conditional probability as it is defined in standard probability theory.


How to Calculate Conditional Probability
Tutorial on how to calculate conditional probability for two events P(A), P(B), P(B|A) with two examples.
The following video gives an introduction to conditional probability.



You can use the Mathway widget below to practice Algebra or other math topics. Try the given examples, or type in your own problem. Then click "Answer" to check your answer.

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