Probability

Question

A city council consists of five Democrats and eight Republicans. If a committee of five people is selected, find the probability of selecting two Democrats and three Republicans.

Answer 1

Use combination:

 

Total Democrats = 5

Total Republicans = 8

Total Democrats + Republicans = 13

 

probability of selecting two democrats = 5C2

probability of selecting three republicans = 8C3

Total # of people selected = 5

 

= (5C2)(8C3) / 13C5

= (10)(56) / 1287

= 560 / 1287

= 0.435 or 0.44 or 44% (Answer)