Question

You are given the probability table below:

_
A A
B 0.12 0.53 0.65
_
B 0.29 0.06 0.35
0.41 0.59 1

Find the following probabilities using the given table:
P(A and B)?

Answer 1

The probability of events A and B occurring together, P(A AND B), is calculated using the formula P(A AND B) = P(B|A) * P(A). With the given probabilities, P(A AND B) is 0.585.

Step-by-step explanation:

The student's question relates to the concept of probability, specifically calculating the joint probability of two events occurring together, denoted as P(A AND B). Using the probability table provided, we are to find the probability that both events A and B occur.

To compute P(A AND B) when knowing the conditional probability P(B|A) and the probability of event A, P(A), we use the formula P(A AND B) = P(B|A) * P(A). It's given that P(B|A) = 0.90 and P(A) = 0.65, so the calculation is as follows:

P(A AND B) = P(B|A) * P(A) = (0.90) * (0.65) = 0.585.

This result means that the probability of both event A and event B occurring together is 0.585.