Question

The management of Young & Sons Sporting Supply, Inc., is responding to a claim of discrimination. If the company has employed the 60 people in the table below, find x so that the age and sex of the people on its staff are independent? S 40 Years>40 Years Total Male Female Total 15 25 20 In a small city, 36% of adults have high blood pressure or high cholesterol. Twenty five percent of the adults have high blood pressure and 20% of the adults have high cholesterol. Find the probability that a randomly chosen adult will have both high blood pressure and high cholesterol.

Answer 1

Question 1

Let no. of people having age>40 and gender: female be x, the table would be:-

	<= 40	>40	Total
Male	25	15	40
Female	20	x	20+x
Total	45	15+x	60+x

If x and y are independent event , then P( x and y) = P(x)* P(y)

so, if sex and age are independent, P( sex = Male and Age>40) = P( sex= Male) * P( Age>40)

$\Rightarrow 15/(60+x) = 40/(60+x) * (15+x)/ ()60+x)$  

$\Rightarrow 15 = 40*(15+x)/(60+x)$

$\Rightarrow 3*(60+x)= 8*(15+x)$

$\Rightarrow 180+3x = 120+ 8x$

$\Rightarrow 5x= 60 \Rightarrow x = 12$

Ans- x=12

Question 2

Let event of an adult chosen having high blood pressure be H

Let event of an adult chosen having high cholesterol be C

Given :-

P(H U C) = 0.36

P(H) = 0.25

P(C) = 0.20

The probability of randomly chosen adult having both high BP and high Cholesterol = P( H and C)

P(H U C) = P(H) + P(C) - P(H and C)

This implies, P(H and C) = P(H) + P(C) - P(H U C)

=>.P(H and C) = 0.25 + 0.20 - 0.36

=>.P(H and C) = 0.09 (i.e 9%)

Ans :- Probability of randomly chosen adult having both high BP and high Cholesterol is 9%