Question

Consider that 80 households purchased a television. The customers were surveyed. Results found that 64 households were satisfied with their purchase and 16 households were dissatisfied. Suppose 2 households are randomly selected from the 80 households. Find the probability that both households are dissatisfied with their purchase. Round to four decimal places. (2 points) Define A = first household selected is dissatisfied Define B = second household selected is dissatisfied.

Answer 1

Answer:

The probability is 0.0380.

For rest of the answer check the explanation.

Step-by-step explanation:

There are in total 80 households who purchased a television.

From the 80 households, 2 households can be chosen in $^{80}C_2 = \frac{80!}{2!\times78!} = 79\times40$ way.

Total 16 households were dissatisfied, hence, from these 16 households 2 households can be chosen in $^{16}C_2 = \frac{16!}{14!\times2!} = 15\times8$ ways.

Hence the required probability is  $\frac{15\times8}{79\times40} = \frac{3}{79} = 0.0380$.

A = first household selected is dissatisfied = the first household is to be chosen from the 16 households. There will be in total 16 possibilities.

B = second household selected is dissatisfied = 16 possibilities if none of the dissatisfied household has been chosen or 15 possibilities if one of these household is already been chosen.