Question

Suppose that A and B are events defined on a common sample space

and that the following probabilities are known: P(A) = 0.4 , P(B) =
0.3 and P(A or B) = 0.66. Find P(A|B).

Answer 1

To calculate the conditional probability P(A|B), we first determined P(A AND B) to be 0.04 by using the formula for the probability of the union of two events. We then divided P(A AND B) by P(B) to find P(A|B), which resulted in 0.1333 or 13.33%.

Step-by-step explanation:

The question asks to find the conditional probability of event A given event B, which is represented as P(A|B). The known probabilities are P(A) = 0.4, P(B) = 0.3, and P(A OR B) = 0.66. Using the formula for the probability of the union of two events, we have P(A OR B) = P(A) + P(B) - P(A AND B), which can be rearranged to find P(A AND B). Once we find P(A AND B), we can calculate P(A|B) using the formula P(A|B) = P(A AND B) / P(B).

First, we'll find the probability of A and B occurring together:

1. P(A OR B) = P(A) + P(B) - P(A AND B)
2. 0.66 = 0.4 + 0.3 - P(A AND B)
3. 0.66 = 0.7 - P(A AND B)
4. P(A AND B) = 0.7 - 0.66
5. P(A AND B) = 0.04

Now we can find P(A|B):

1. P(A|B) = P(A AND B) / P(B)
2. P(A|B) = 0.04 / 0.3
3. P(A|B) = 0.1333

Therefore, the conditional probability of event A given event B, P(A|B), is 0.1333, or 13.33%.