Suppose that A and B are events defined on a common sample space and that the following probabilities are known. Find P(A or B). (Give your answer correct to two decimal places.)
P(A) = 0.32, P(B) = 0.36, P(A | B) = 0.24
To find P(A or B), we can use the formula:
P(A or B) = P(A) + P(B) - P(A and B)
First, we have P(A) = 0.32 and P(B) = 0.36.
Next, to find P(A and B), we need to use conditional probability and the formula:
P(A and B) = P(B) * P(A | B)
Given that P(A | B) = 0.24, we can substitute the values into the formula:
P(A and B) = 0.36 * 0.24 = 0.0864
Now, we have all the values needed to calculate P(A or B):
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.32 + 0.36 - 0.0864
P(A or B) = 0.594
Therefore, P(A or B) = 0.59 (correct to two decimal places).