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A total of 500 married working couples were polled about their annual salaries, with the following information resulting:

For instance, in 36 of the couples, the wife earned more and the husband earned less than \( 25,000. If one of the couples is randomly chosen, what is

(a) the probability that the husband earns less than \) 25,000 ?

(b) the conditional probability that the wife earns more than \( 25,000 given that the husband earns more than this amount?

(c) the conditional probability that the wife earns more than \) 25,000 given that the husband earns less than this amount?

Short Answer

Expert verified

a. The probability that the husband earns less than $ 25,000 is 0.496.

b. The conditional probability that the wife earns more than $ 25,000 given that the husband earns more than this amount is 0.214.

c. The conditional probability that the wife earns more than $ 25,000 given that the husband earns less than this amount is0.145.

Step by step solution

01

Given Information

500married couples were surveyed about their annual earnings.

02

Formula Used 

Probability of an event=Number of favorable outcomesNumber of total outcomes

03

Calculation (Part a) 

Couples in which the husband earns less than$25,000=212+36=248

The probability that the husband earns less than $ 25,000=248500=0.496

04

Calculation (Part b)

Couples in which husbands more than$25,000=198+54=252

Couples in which the wife earns more than$25,000given the husband earns more than$25,000=54

Probability that the wife earns more than$25,000given the husband earns more than this amount=54252=314=0.214

05

Calculation (Part c)

Couples in which husbands less than$25,000=212+36=248

Couples in whichthe wife earns more than$25,000given the husband earns less than this amount=36

Probability that the wife earns more than$25,000given the husband earns less than this amount=36248=962=0.145

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