Given P(A) = 0.5, P(B) = 0.3 and P(C) = 0.2
\(\therefore\) P(A) + P(B) + P(C) = 1
then events A, B, C are exhaustive.
If P(E) = Probability of introducing a new product, then as given
P(E|A) = 0.7, P(E|B) = 0.6 and P(E|C) = 0.5
= 0.5 \(\times\) 0.7 + 0.3 \(\times\) 0.6 + 0.2 \(\times\) 0.5 = 0.35 + 0.18 + 0.10 = 0.63
The probability of India winning a test match against the west indies is 1/2 assuming independence from match to match. The probability that in a match series India’s second win occurs at the third test is