A charter boat company of St. Lucia takes tourists on a daily dolphin/whale watc

Question

A charter boat company of St. Lucia takes tourists on a daily dolphin/whale watch cruise. Their brochure claims an 85% chance of sighting a whale or a dolphin. Suppose there is a 71% chance of seeing dolphins and a 14% chance of seeing both dolphins and whales. Make a Venn diagram. Then answer these questions. (a) What is the probability of seeing a whale on the cruise? (Enter your answer to two decimal places.) (b) What is the probability of seeing a whale but not a dolphin? (Enter your answer to two decimal places.) (c) Are "seeing a whale" and "seeing a dolphin" independent events? Yes, the events are independent. No, the events are not independent.

Explanation / Answer

(a)Given that P(Whale or dolphin)=0.85, P(D)=0.71, P(W and D)=0.14

Now, P(W or D)=0.85

P(W)+P(D)-P(W and D)=0.85

P(W)+0.71-0.14=0.85

P(W)=0.85-0.71+0.14=0.28

(b)P(W but not a D)

=P(W)-P(W and D)

=0.28-0.14

=0.14

(c)No, the two events seeing whale and seeing dolphin are not independent.

P(W and D)=0.14 which is not equal to P(W)*P(D)=0.28*0.71=0.1988

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