The Probability of Choosing Chocolate Ice Cream: A Statistical Analysis

[nmnicw]

How can I solve this?

It is known in the ice-cream industry that 38% of people have chocolate as their favourite flavour of ice-cream.

Let X be the number of people in a sample of 10 who say chocolate is their favourite ice-cream flavour.

Find P(X < 3)

Do I need to use the probability tree to list all the probability out?

 

[HallsofIvy]

This certainly should NOT be in the "Calculus and Beyond" section- no Calculus required.
I would NOT use a "probability tree". Just ask youself, if I were to ask each person which flavour they prefer, what is the probability the first person would say "chocolate"? What about the second and third? That's easy- they are all the 38%= 0.38 you are given. Now, having done that, What is the probability the next 7 people, 4 though 10, would say anything other than chocolate? Again, that's easy- they are all the same. Just multiply those 10 numbers together to get the probability of exactly that result.

But that was in that particular order. To allow for say, "CNCNNNCNNN" (here, "C" indicates "said Choclolate" and "N" indicates "did not say Chocolate"), rather than "CCCNNNNNNN", as above, multiply by the number of ways of order 3 "C"s and 7 "N"s- that's a binomial coefficient.

That will give the probability that exactly 3 people say their favorite is Choclolate. Now do the same with "CCNNNNNNNN", "CNNNNNNNNN", and "NNNNNNNNNN" and add them together to get "3 or less".

 

[Leptos]

You're given p = .38, n = 10, k = 0, 1, 2.
Take the summation of the binomial probability distribution from k = 0 to k = 2 and you get the value for p(X < 3)