Question 1086241: You are recruiting volunteers for a study on food choices at the grocery store. You need 32 participants, but you have 47 who apply to participate in the study.
a. How many different groups of 32 participants can you select from those who applied?
b. If three of the applicants are vegans, what is the probability of randomly selecting at least one vegan for the study?
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website! Question:
You are recruiting volunteers for a study on food choices at the grocery store. You need 32 participants, but you have 47 who apply to participate in the study.
a. How many different groups of 32 participants can you select from those who applied?
b. If three of the applicants are vegans, what is the probability of randomly selecting at least one vegan for the study?
Solution:
(a) 47 choose 32 = C(47,32) = 47!/(32!(47-32)!)=751616304549
(b) Within each group, we're choosing at least one vegan out of three.
The probability
P(>=1)
=1-P(0)
=1 - (47-3)choose32/47choose32
=1-C(44,32)/C(47,32)
=1-91/3243
=3152/3243
(=0.9719 approx.)
|
|
|
