Question

A jury pool consists of 6 men and w women. If 2 jurors are selected from the pool at random, is the probability that 2 men will be selected higher than the probability that 1 man and 1 woman will be selected?

Answer 1

Answer:

Yes, it is higher if w ≥ 3.

Explanation:

Given,

Number of men = 6,

Number of women = w,

Ways of choosing 2 men = C(6,2),

There can be two cases,

Case 1 :

If w ≥ 3,

Then the number of ways of choosing 1 men and 1 women > Ways of choosing two men,

So, the probability of choosing 1 men and 1 women is greater than that of choosing two men,

For eg : If w = 8,

$^8C_1\times ^6C_1>^6C_2$

$\implies \frac{^8C_1\times ^6C_1}{^{14}C_2}>\frac{^6C_2}{^{14}C_2}$

Similarly if w = 3,

$\implies \frac{^3C_1\times ^6C_1}{^{14}C_2}>\frac{^6C_2}{^{14}C_2}$

Case 2 :

If 0 < w < 3,

Then the number of ways of choosing 1 men and 1 women < Ways of choosing two men,

So, the probability of choosing 1 men and 1 women is less than that of choosing two men

eg :

$\frac{^2C_1\times ^6C_2}{^{14}C_2}$