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

Yes, it is higher if w ≥ 3.

Step-by-step 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* ^6C_1>^6C_2`

`\implies (^8C_1* ^6C_1)/(^(14)C_2)>(^6C_2)/(^(14)C_2)`

Similarly if w = 3,

`\implies (^3C_1* ^6C_1)/(^(14)C_2)>(^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 :

`(^2C_1* ^6C_2)/(^(14)C_2)<(^6C_2)/(^(14)C_2)`