Question

In a large bag of Skittles, an individual finds that there are 9 Green, 11 Orange, 13 Red, 7 Yellow, and 11 Purple Skittles. If the individual selects 6 Skittles at random without replacement, find the following probabilities. Show your work to receive credit.

a. P(3 are Green)

b. P(2 red and 3 purple)

Answer 1

Combination formula to select r items from n, nCr = n!/(r! x (n-r)!)

Total number of Skittles = 9 + 11 + 13 + 7 + 11 = 51

a. P(3 are Green) = Number of ways to select 3 green Skittle from 9 x Number of ways to select 3 other Skittles from 42 / Number of ways to select any 6 Skittles from 51

= 9C3 x 42C3 / 51C6

= 84 x 11,480 / 18,009,460

= 0.0535

b. P(2 red and 3 purple) = Number of ways to select 2 red from 13 x Number of ways to select 3 purple from 11 x Number of ways to select 1 other from remaining 27 / Number of ways to select any 6 Skittles from total 51

= 13C2 x 11C3 x 27C1 / 51C6

= 78 x 165 x 27 / 18,009,460

= 0.0193