Question

Given P(A) = 0.3, P(B) = 0.6, and P(A|B) = 0.1, determine the following probabilities.

(a). P(A and B) =

(b) P(A or B) =

Answer 1

To find P(A and B), we multiply P(A|B) by P(B), resulting in 0.06. P(A or B) is computed using the formula for the union of two events, resulting in 0.84.

Step-by-step explanation:

The student asked to determine the probabilities of P(A and B) and P(A or B), given that P(A) = 0.3, P(B) = 0.6, and P(A|B) = 0.1.

To find P(A and B), we use the definition of conditional probability: P(A|B) = P(A and B) / P(B). This yields P(A and B) = P(A|B) * P(B) = 0.1 * 0.6 = 0.06. For P(A or B), we use the formula for the probability of the union of two events: P(A or B) = P(A) + P(B) - P(A and B), giving us P(A or B) = 0.3 + 0.6 - 0.06 = 0.84.