4.Are you really being served red snapper?Red snapper is a rare and expensive reef fish served at 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 butthe cheaper look-alike variety of fish.a.Assuming 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 at a restaurant?b.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?

Assuming the results of the DNA analysis are valid, the probability that you are actually served red snapper the next time you order it at a restaurant is:

P (Being served Red Snapper) = 0.23.

Thus, the probability of being served Red Snapper is 0.23.

(b)

The random variable X follows a binomial distribution with parameters n = 5 and p = 0.23.

The probability distribution of binomial is:

[tex]P(X =x)={n\choose x}p^{x}(1-p)^{n-x}[/tex]

If there are 5 customers at a restaurant ordering red snapper, the probability that at least one customer is actually served red snapper is:

P (X ≥ 1) = 1 - P(X < 1)

= 1 - P (X = 0)

[tex]=1-{5\choose 0}(0.23)^{0}(1-0.23)^{5-0}\\=1-(1\times1\times0.2707)\\=1-0.2707\\=0.7293[/tex]

Thus, the probability that at least one customer of 5 is actually served red snapper is 0.7293.