Question

. A discount bin contains 5 identical red gloves, 7 identical brown gloves and 8 identical blue gloves. A shopper grabs two of them randomly. a. What is the sample space for this experiment? b. What is the probability that the gloves selected are the same color?

Answer 1

Combination formula: nCr = n!/(r! x (n-r)!)

a. Let R indicare red glove, W indicate brown glove and B indicate blue glowe.

Then, sample space, S = {RR, RW, RB, WW, WB, BB}

b. Number of red gloves = 5

Number of brown gloves = 7

Number of blue gloves = 8

Total number of gloves = 20

P(the gloves selected are of same color) = (Number of ways to select 2 red from 5 + Number of ways to select 2 brown from 7 + Number of ways to select 2 blue from 8) / Number of ways to select any 2 from 20

= (5C2 + 7C2 + 8C2) / 20C2

= (10 + 21 + 28) / 190

= 0.3105