(a). Can a binomial distribution be used for the solution of the above problem?
According to binomial distribution concept, The binomial distribution can be used when the result of each experiment in the process are yes/no or success/failure.
That means, binomial distribution express the probability of one set of dichotomous alternatives, means as success or failure, from a fixed number of trials.
In this question, does not use binomial distribution probability because there are only talk about chooses the entrée from seven entrée.
(b). What kind of probability distribution can be used to solve this problem?
According to the question, here use simple probability distribution.
(c). What is the probability that both members chose vegetarian entrées?
The total number of entrée is 7.
From these entrees there are two of the entrée choices are vegetarian.
The probability that both members chose vegetarian entrées
Hence, the probability that both members chose vegetarian entrees is 0.020.