There are 23 families living in the Willbrook Farms Development. Of these families, 10 prepared their...

There are 23 families living in the Willbrook Farms Development. Of these families, 10 prepared their own federal income taxes for last year, 5 had their taxes prepared by a local professional, and the remaining 8 by H&R Block.

What is the probability of selecting a family that prepared their own taxes? (Round your answer to 2 decimal places.)
What is the probability of selecting two families, both of which prepared their own taxes? (Round your answer to 4 decimal places.)
What is the probability of selecting three families, all of which prepared their own taxes? (Round your answer to 4 decimal places.)
What is the probability of selecting two families, neither of which had their taxes prepared by H&R Block? (Round your answer to 4 decimal places.)

Expert Solution

(a) What is the probability of selecting a family that prepared their own taxes? (Round your answers to 3 decimal places.)

Probability = Families prepared own taxes/Total Families

10/23 = 0.4347826

(b) What is the probability of selecting two families both of which prepared their own taxes? (Round your answers to 3 decimal places.)

After selecting the first person from own tax families there will only remain 9 own tax family and 22 total families.

Probability = (10 / 23)(9 / 22) = 0.1778656

(c) What is the probability of selecting three families, all of which prepared their own taxes? (Round your answers to 3 decimal places.)

Probability = (12 / 24)(11 / 23)(9 / 21) = 0.1024845

(d) What is the probability of selecting two families, neither of which had their taxes prepared by H&R Block? (Round your answers to 3 decimal places.)

There are 23-8 = 15 families who have not prepared taxes by H&R department.

The probability of selecting two families from these above 15 families = probability of selecting two families, neither of which had their taxes prepared by H&R Block.

Probability = (15/ 23)*(14 / 22) = 0.4150198

orchestra answered 2 years ago

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