Question

There are 20 families living in the Willbrook Farms Development. Of these families 10 prepared their own federal income
taxes for last year, 7 had their taxes prepared by a local professional, and the remaining 3 by H&R Block.
a.What is the probability of selecting a family that prepared their own taxes?
b.What is the probability of selecting two families, both of which prepared their own taxes?
c.What is the probability of selecting three families, all of which prepared their own taxes?
d.What is the probability of selecting two families, neither of which had their taxes prepared by H&R Block?

Answer 1

Answer:

(a) The probability of selecting a family that prepared their own taxes is 0.50.

(b) The probability of selecting 2 families that prepared their own taxes is 0.2368.

(c) The probability of selecting 3 families that prepared their own taxes is 0.1053.

(d) The probability of selecting 2 families such that neither of which had their taxes prepared by H&R Block is 0.7158.

Step-by-step explanation:

Total number of families living in the Will brook Farms Development is, N = 20.

The number of families that prepared their own federal income  taxes is, n (O) = 10

The number of families that had their taxes prepared by a local professional is, n (L) = 7

The number of families that had their taxes prepared by H&R Block is, n (H) = 3.

(a)

Compute the probability of selecting a family that prepared their own taxes as follows:

$P(O)=\frac{n(O)}{N} =\frac{10}{20}=0.50$

Thus, the probability of selecting a family that prepared their own taxes is 0.50.

(b)

Compute the probability of selecting 2 families that prepared their own taxes as follows:

P (2 families ∩ O) = P (1st family ∩ O) + P (2nd family ∩ O)

                             $=\frac{10}{20}\times\frac{9}{19} \\=0.2368$

Thus, the probability of selecting 2 families that prepared their own taxes is 0.2368.

(c)

Compute the probability of selecting 3 families that prepared their own taxes as follows:

P (3 families ∩ O) = P (1st family ∩ O) + P (2nd family ∩ O)

                                           + P (3rd family ∩ O)

                             $=\frac{10}{20}\times\frac{9}{19}\times\frac{8}{18} \\=0.1053$

Thus, the probability of selecting 3 families that prepared their own taxes is 0.1053.

(d)

Compute the probability of selecting 2 families such that neither of which had their taxes prepared by H&R Block as follows:

P (2 families ∩ not H) = P (1st family ∩ not H) + P (2nd family ∩ not H)

                                   = [1 - P (1st family ∩ H)] + [1 - P (2nd family ∩ H)]

                                   $=[1-\frac{3}{20}]\times[1-\frac{2}{19}]\\=\frac{17}{20}\times\frac{16}{19}\\=0.7158$

Thus, the probability of selecting 2 families such that neither of which had their taxes prepared by H&R Block is 0.7158.