Question

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The "starting five" for a hockey team consists of two guards, two forwards, and one center. Two starting players will be selected at random to serve as team captains for the game. (report all answers to this question as unreduced fractions, example: 13/20) What is the probability that the two captains are both guards? What is the probability that at least one of the captains is a guard? What is the probability that the starting center is a captain? What is the probability that the two captains play the same position?

Answer 1

Answer:

Given,

Sample n = 2

A = 2 , B = 2 , C = 1

nCr = n! / (n-r)!*r!

a)

P(Two captains are both guards) = P(X = 2)

= 2C2 / 5C2

= 1 / 10

= 0.1

b)

P(At least 1) = P(X >= 1)

= [(2C1*2C1*1C0) + (2C1*2C0*1C1)] / 5C2

= [2*2*1 + 2*1*1] / 10

= 6/10

= 0.6

c)

P(X = 1) = 1C1 / 5C2

= 1/10

= 0.1

d)

P(Two captains play same position) = [2C2*2C0*1C0 + 2C0*2C2*1C0] / 5C2

= 2/10

= 1/5

= 0.2