Question

In: Statistics and Probability

In a sample of 1000 recent MBA graduates, 700 said they earnover $100,000 per year,...

In a sample of 1000 recent MBA graduates, 700 said they earn over $100,000 per year, 300 said that 100% of their health insurance premiums are paid by the company for which they work, and 100 said that they neither earn over $100,000 per year, nor does their company pay 100% of their health insurance premiums. Compute the probability of a recent MBA graduate earning over $100,000 per year and having 100% of their health insurance premiums.

Solutions

Expert Solution

Let A be the event of earning over $100,000 per year and B be the event of paying 100% of their health insurance premiums being paid by the company.

As we know the sample is 1000. So,

P(A) = 700/1000

= 0.7

P(B) = 300/1000

= 0.3

P(A' B') = 100/1000

= 0.1

We know that,

P(A' B') = P(A B)'

= 1 - P(A B)

So,

P(A B) = 900/1000

= 0.9

We also know,

P(A B) = P(A) + P(B) - P(A B)

So,

P(A B) = 0.7 + 0.3 - 0.9

= 0.1

Thus the probability of a recent MBA graduate earning over $100,000 per year and having 100% of their health insurance premiums = 0.1

orchestra answered 2 years ago
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