Question

At a town fair, everyone who wins one of the contests selects a prize. There are 14 prizes available, including 7 pies, 4 gift certificates, 2 fruit baskets, and 1 bicycle. (Suppose all prizes are equally valuable to each conestant.)

What is the probability that the first 3 winners will all select gift certificates?






What is the probability that the first winner will select either a pie or a fruit basket?

Answer 1

Problem 1

A = probability 1st winner picks gift certificate (no replacement)

A = 4/14 = 2/7

B = probability 2nd winner picks gift certificate (no replacement)

B = 3/13

C = probability 3rd winner picks gift certificate (no replacement)

C = 2/12 = 1/6

D = probability first 3 winners pick gift certificate (no replacement)

D = A*B*C

D = (2/7)*(3/13)*(1/6)

D = (2*3*1)/(7*13*6)

D = 6/546

D = 1/91 is the final answer

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Problem 2

A = probability 1st winner picks pie

A = 7/14

B = probability 1st winner picks fruit basket

B = 2/14

C = probability 1st winner picks pie OR fruit basket

C = A+B

C = 7/14 + 2/14

C = 9/14 is the final answer