A total of 500 married working couples were polled about their annual salaries,

ID: 3295280 • Letter: A

Question

A total of 500 married working couples were polled

about their annual salaries, with the following information resulting.

In 212 cases both partners made less than $50,000.

In 198 cases the husband made more and the wife less than $50,000.

in 36 cases the wife made more and the husband less than $50,000.

In 54 cases both partners made more $50,000.

1. What is the probability that the husband makes less than $50,000?

2. What is the conditional probability that the wife makes makes more

than $50,000 given that the husband makes more than this amount?

3. What is the conditional probability that the wife makes more than

$50,000 given that the husband makes less than this amount?

Here we have:

212 cases both partners made less than $50,000 which could be represented as:

n( both ) = 212

Similarly other conditions given are:

n(wife only) = 198

n(husband only) = 36

n( neither ) = 54

1) Probability that the husband makes less than 50,000

= [ n(husband only) + n(both) ] / Total people

= ( 36 + 212 ) / 500

= 0.496

Therefore 0.496 is the required probability here.

2) Conditional probability that the wife makes makes more than $50,000 given that the husband makes more than this amount?

Using bayes conditional probability formula this could be computed as:

= n( neither ) / [ n( wife only ) + n(neither ) ]

= 54/ (54 + 198)

= 0.2143

Therefore 0.2143 is the required probability here.

3) Conditional probability that the wife makes more than $50,000 given that the husband makes less than this amount?

Again using the bayes theorem we get:

= n( husband only ) / [ n(both) + n(husband only ) ]

= 36 / (36 + 212)

= 0.1452

Therefore 0.1452 is the required probability here.

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