Question

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

Answer 1

The probability of selecting three Democrats and two Republicans is 0.36

Explanation:

Given:

The Number of Democrats = 7

The Number of Republicans = 7

To Find:

Probability of selecting three Democrats and two Republicans. = ?

Solution:

we have to select a committee of 5 people

Now the probability of selecting three Democrats and two Republicans.

=>
`\frac{\mathrm{P}(\text { Selecting three Democrats }) \cdot \mathrm{P}(\text { Selecting three Republicans })}{\mathrm{P}(\text { Selecting } 5 \text { member from total } 14)}`

=>
`(C(7,3) \cdot C(7,2))/(C(14,5))`

=>
`(7 C_(3) \cdot 7 C_(2))/(14 C_(5))`

=>
`(35\cdot 21)/(2002)`

=>
`(735)/(2002)`

=>0.36