Question

Of the 25 people invited to a birthday party, 5 prefer vanilla ice cream, 8 prefer chocolate, and 4 prefer strawberry. The host surveys 6 of these people at random to determine how much ice cream to buy.
a. what is the probability that at least 3 of the people surveyed prefer chocolate ice cream?
b. what is the probability that none prefer vanilla?
c. what is the expected number of people who prefer strawberry?
d. what is the expected number of people who do not have a preference for any of the three flavours?

Answer 1

(a) p = 8/25 , n = 6

P(x > =3)
= 1 - P(x< 3)
= 1- [P(x=0)+P(x=1)+P(x=2)]
= 1 - [6c0 * (8/25)^0 *( 17/25)^6 +6c1 * (8/25)^1 * ( 17/25)^5 +6c2 *(8/25)^2 *(17/25)^4 ]
= 0.2935

Answer 2

ok I understand that. What about b?

Answer 3

\[P(0\ vanilla)=6C0\times (\frac{4}{5})^{6}=you\ can\ calculate\]