Given that P(A)=0.81 and P(B|A)=0.23, find the joint probability P(A and B):
well ... know your definitions
P(B|A) = P(A and B) / P(B|A)
.23 = P(A and B) / .81
P(A and B) = (.23)(.81) = ....
To find the joint probability P(A and B), we can use the formula for conditional probability:
P(A and B) = P(A) * P(B|A)
Given that P(A) = 0.81 and P(B|A) = 0.23, we can substitute these values into the formula:
P(A and B) = 0.81 * 0.23
Calculating this expression:
P(A and B) ā 0.1863
Therefore, the joint probability P(A and B) is approximately 0.1863.