Let A and B denote the events that the man wins contracts X and Y...

Explanation

Let A and B denote the events that the man wins contracts X and Y respectively.

Then P(A) = 0.5

P(A') = 1 - 0.5 = 0.5

P(B') = 0.3

P(B) = 1 - 0.3 = 0.7

(a) The probability that the man wins both contracts = \(0.5 \times 0.7 = 0.35\).

(b) The probability that the man wins exactly one of the contracts is \(P(A) \times P(B') + P(B) \times P(A')\)

= \(0.5 \times 0.3 + 0.7 \times 0.5\)

= \(0.15 + 0.35\)

= \(0.50\)

(c) Neither of the contracts (i.e not X, not Y) = \(P(A') \times P(B')\)

= \(0.5 \times 0.3\)

= \(0.15\)