There are three probabilities for preferring Product A, Product B, and Product C

Question

There are three probabilities for preferring Product A, Product B, and Product C. Ten people sampled all three products and provided his/her preference.

Prob. (Prefer Product A) = 3/10

Prob. (Prefer Product B) = 5/10

Prob. (Prefer Product C) = 2/10

Then, the participants were all asked to try to identify the one he/she preferred. Some participants correctly identified the product, while others incorrectly identified the product. Here are the joint and marginal probabilities below:

QUESTION: If Product A is the number of people in the sample who preferred Product A, using the above data, what is A and 2A ?

Explanation / Answer

here as this is binomial distribtuion wtih paramter of probability who preferred product A p =3/10 and n=10

hence A =np=10*(3/10) =3

and 2A =np(1-p) =10*(3/10)*(1-3/10)=21/10=2.1

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