A restaurant menu lists seven entrée choices. Two of the entrée choice

achieverh3 2021-11-20 Answered
A restaurant menu lists seven entrée choices. Two of the entrée choices are vegetarian. One member of a couple chooses one entrée at random and then the other member chooses a different entrée at random. Consider the problem of calculating the probability that the couple choose vegetarian entrées.
- Can a binomial distribution be used for the solution of the above problem? Why or why not?
- What kind of probability distribution can be used to solve this problem?
- What is the probability that both members chose vegetarian entrées?

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Expert Answer

Melinda Olson
Answered 2021-11-21 Author has 1799 answers

(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.
So,
In this question, does not use binomial distribution probability because there are only talk about chooses the entrée from seven entrée.
Step 2
(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?
Then
The total number of entrée is 7.
From these entrees there are two of the entrée choices are vegetarian.
So,
The probability that both members chose vegetarian entrées
\(\displaystyle{P}{\left({v}{e}ge{t}{a}{r}{i}{a}{n}\right)}={\frac{{{1}}}{{{7}}}}\cdot{\frac{{{1}}}{{{7}}}}\)
\(\displaystyle={0.020}\)
Hence, the probability that both members chose vegetarian entrees is 0.020.

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