The probability that it rains on a certain day is 0.3. If it rains, the probability that a cricket match is held that day is 0.4; if it does not rain, this probability is 0.9. The probability that the match is held that day is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 0.75
Let \(E_1\) be the event that it rains, \(E_2\) that it does not, and A that the match is held.
\(P(E_1) = 0.3,\quad P(A|E_1) = 0.4\)
\(P(E_2) = 0.7,\quad P(A|E_2) = 0.9\)
By the theorem of total probability:
\(P(A) = 0.3\times 0.4 + 0.7\times 0.9\)
\(P(A) = 0.12 + 0.63 = 0.75\)