15. Red snapper is a rare and expensive reef fish served in upscale restaurants.

Question

15. Red snapper is a rare and expensive reef fish served in upscale restaurants. Federal law prohibits restaurants from serving a cheaper, look-alike variety of fish (e.g. vermillion snapper or lane snapper) to customers who order red snapper. Researchers at the University of North Carolina used DNA analysis to examine fish specimens labeled "red snapper" that were purchased from vendors across the country. The DNA tests revealed that 77% of the specimens were not red snapper, but the cheaper, look-alike variety of fish. Assuming that the results of the DNA analysis are valid, what is the probability that you are actually served red snapper the next time you order it ata restaurant? The probability of red snapper equals 1-0.77-0.23 If there are five customers at a restaurant, all who have ordered red snapper, what is the probability that at least one customer is actually served red snapper? The probability that at least one customer out of five is served red snapper equals 1-(0.77)s = 0.7293. a. b.

Explanation / Answer

A)

The probability of not serving red snapper is 0.77.

The probability of serving red snapper is

P(serving red snapper)=1-p(not serving red snapper)

=1-0.77

=0.23

B) Binomial with n = 5 and p = 0.23 [that is, the probability it is red snapper]
P(at least one is red snapper) = 1 - P(none are red snapper)
= 1 - 5C0(0.23)0 (1-0.23)5

=1 - 0.2707

=0.7293

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