The grammar has been fixed, and unnecessary words removed: Two number cubes are rolled in separate events. Event A occurs when the sum of the numbers on both cubes is less than 10, and Event B occurs when the sum is a multiple of 3. Complete the conditional probability formula for Event B given Event A as follows: P(B | A) = P(A ∩ B) / P(A).
Mathematics · College · Thu Feb 04 2021
Answered on
The conditional probability of Event B given Event A is calculated by finding the probability of both A and B happening divided by the probability of A happening. Using your notation, where A is the event where the sum is less than 10, and B is the event where the sum is a multiple of 3, the formula for the conditional probability of B given A is:
P(B | A) = P(A ∩ B) / P(A)
In this formula, P(A ∩ B) represents the probability of both Event A and Event B occurring simultaneously (the sum is both less than 10 and a multiple of 3). P(A) represents the probability of Event A occurring (the sum is less than 10).