Answer:
The probability of selecting three Democrats and two Republicans is 0.349
Step-by-step explanation:
Given:
The Number of Democrats = 6
The Number of Republicans = 8
To Find:
Probability of selecting 2 Democrats and 4 Republicans. = ?
Solution:
we have to select a committee of 6 people
Now the probability of selecting 2 Democrats and 4 Republicans.
=>[tex]\frac{\mathrm{P}(\text { Selecting two Democrats }) \cdot \mathrm{P}(\text { Selecting four Republicans })}{\mathrm{P}(\text { Selecting } 6 \text { member from total } 14)}[/tex]
=>[tex]\frac{C(6,2) \cdot C(8,4)}{C(14,6)}[/tex]
=>[tex]\frac{ 6 C_{2 } \cdot 8 C_{4}}{14 C_{6}}[/tex]
=>[tex]\frac{15\cdot 70}{3003}[/tex]
=>[tex]\frac{1050}{3003}[/tex]
=>0.349
