Question

Please solve the following question.

Answer 1

The chance of selecting 10 men is unlikely in a random selection

The probability that the jury is made of 2 men

The given parameters are:

• Men = 17
• Women = 15
• Total = 32

The total number of selections is:

$Total = ^{32}C_{10}$

Evaluate

Total = 64512240

If 2 men are selected, then 8 women would be selected.

So, the number of ways is:

$Ways = ^{17}C_2 * ^{15}C_8$

Evaluate

Ways = 136 * 6435

Ways = 875160

The required probability is:

P = 875160/64512240

P = 0.0136

Hence, the probability that the jury is made of 2 men is 0.0136

The probability that half the jury are men

If 5 men are selected, then 5 women would be selected.

So, the number of ways is:

$Ways = ^{17}C_5 * ^{15}C_5$

Evaluate

Ways = 6188 * 792

Ways = 4900896

The required probability is:

P = 4900896/64512240

P = 0.0760

Hence, the probability that the jury is made of half men and women is 0.0760

The probability that at least two women are selected

To do this, we make use of the complement rule:

P = 1 - P(Not up to 2 is selected)

When 0 women are selected, then 10 men are selected and when 1 woman is selected, then 9 men are selected

So, the number of ways is:

$Ways = ^{17}C_{10} * ^{15}C_0 + ^{17}C_{9} * ^{15}C_1$

Evaluate

Ways = 19448 * 1 + 24310 * 15

Ways = 384098

The probability P(Not up to 2 is selected) is:

P = 0.0060

The required probability is:

P = 1 - 0.0060

P = 0.9940

Hence, the probability that the jury is made of at least two women is 0.9940

The probability that at 10 men are selected

When 10 men are selected, then 0 women are selected

So, the number of ways is:

$Ways = ^{17}C_{10} * ^{15}C_0$

Evaluate

Ways = 19448 * 1

Ways = 19448

The probability is:

P = 19448/64512240

P = 0.0003

Hence, the probability that the jury is made of 10 men is 0.0003

The selection above can lead to suspicion because the chance of selecting 10 men is unlikely in a random selection

Read more about probability at:

brainly.com/question/251701

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