(a) If both ships sent to the same destination

State

Probability

Payoff

Expected payoff

Both ships arrive

0.9 = 90%

£2,000

(0.9 × £2,000) + (0.1 × £0) = £1,800

Both ships lost

0.1 = 10%

0

(b) If one ship sent east, one west

State

Probability

Payoff

Expected payoff

Both ships arrive

0.9 × 0.9 = 81%

£2,000

Both ships lost

0.1 × 0.1 = 1%

0

(0.81 × £2,000) + (0.01 × £0) + (0.18 × £1,000) = £1,800

One ship arrives

(0.9 × 0.1) + (0.1 × 0.9) = 18%

1,000