Question

PLEASE NOTE I DO NOT UNDERSTAND THE SOLUTION GIVEN FROM THE BOOK SO CAN YOU DO IT PLEASE

A panel of 300 persons chosen for jury duty includes 30 under 25 years of age. Since the jury of 12 persons chosen from this panel to judge a drug violation does not include anyone under 25 years of age, the youthful defendant’s attorney complains that this jury is not really representative. Indeed she argues, if the selection were random, the probability of having one of the 12 jurors under 25 years of age should be many times the probability of having none of them under 25 years of age. What is the ratio of these two probabilities?

Answer 1

Solution:

total number of persons = 300

number of persons under 25 years of age = 30

p = 30 / 300 = 0.10

number of persons selected as jury = n = 12

binomial probability distribution

Formula:

P_{(k out of n )}= n!*p^k * q^n-k / k! *(n - k)!

probability of selecting one person under 25 years age out of 12 person jury = P( x = 1 ) = 12!*0.1¹ * 0.9^12-1 / 1! *(12 - 1)!

= 0.3766

probability of selecting no person under 25 years age out of 12 person jury = P( x = 0 ) = 12!*0.1⁰ * 0.9^12-0 / 0! *(12 - 0)!

= 0.2824

Ratio of these two probabilities = P( x = 1 ) / P( x = 0) = 0.3766 / 0.2824 = 1.3335