Answer:
The probability of selecting three Democrats and two Republicans is 0.36
Step-by-step 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.
=>[tex]\frac{\mathrm{P}(\text { Selecting three Democrats }) \cdot \mathrm{P}(\text { Selecting three Republicans })}{\mathrm{P}(\text { Selecting } 5 \text { member from total } 14)}[/tex]
=>[tex]\frac{C(7,3) \cdot C(7,2)}{C(14,5)}[/tex]
=>[tex]\frac{7 C_{3} \cdot 7 C_{2}}{14 C_{5}}[/tex]
=>[tex]\frac{35\cdot 21}{2002}[/tex]
=>[tex]\frac{735}{2002}[/tex]
=>0.36
