Question-9

Let \(A\) and \(B\) be the two events of a random experiment. Probability that at least one of the two events \(A\) and \(B\) will occur is 0.6. Probabilities of event \(A\) occurring and \(B\) occurring are 0.3 and 0.4 respectively. Then, find the probability that event \(A\) will occur given that event \(B\) has occurred.

Hint

Use addition rule of probability to calculate \(P(A \cap B)\) and then apply the conditional probability formula.

Answer

0.25

Solution

Given, \(P(A) = 0.3, P(B) = 0.4\) and \(P(A \cup B) = 0.6\)
\(P(A \cap B) = P(A) + P(B) - P(A \cup B) = 0.3 + 0.4 - 0.6 = 0.1\)

\(P(A | B) = \dfrac{P(A \cap B)}{P(B)} = \dfrac{0.1}{0.4} =\dfrac{1}{4} = 0.25\).