Of twenty people invited to a party, 4 prefer vanilla ice cr

[kimmy_koo51]

Of twenty people invited to a party, 4 prefer vanilla ice cream, 7 prefer chocolate, and 3 strawberry. The hosts survey six 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 ice cream?
c. What is the expected number of people who prefer strawberry ice cream?
d. What is the expected number of people who do not have a preference for any of these flavors?

I know how to do all of these using the formulas. I just have no idea how to identify the variables. I always get them mixed up. (n, r, a, and x)

Please some help would be greatly appreciated.

Thank you very much in advance.

 

[galactus]

Re: Of twenty people invited to a party, 4 prefer vanilla ic

Of twenty people invited to a party, 4 prefer vanilla ice cream, 7 prefer chocolate, and 3 strawberry. The hosts survey six 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?

I know how to do all of these using the formulas. I just have no idea how to identify the variables. I always get them mixed up. (n, r, a, and x)

Please some help would be greatly appreciated.

Thank you very much in advance.

Appears you can use a binomial.

7 of the 20 prefer chocolate. So we have:

\(\displaystyle \L\\\sum_{k=3}^{6}C(6,k)(\frac{7}{20})^{k}(\frac{13}{20})^{6-k}\)