Question

.A survey was conducted by a consulting company. Results showed that 83% of their previous customers would recommend the company to other businesses.
What is the probability that two independent customers would recommend the consulting company? Round to four decimal places. (1 point)
What is the probability that one of the two customers would recommend the consulting company [P(A or B)]? Round to four decimal places. (1 point)

Answer 1

Answer:

0.6889 = 68.89% probability that two independent customers would recommend the consulting company.

0.2822 = 28.22% probability that one of the two customers would recommend the consulting company.

Step-by-step explanation:

For each customers, there are only two possible outcomes. Either they would recommend the company to other businesses, or they would not. The customers are independent. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Results showed that 83% of their previous customers would recommend the company to other businesses.

This means that $p = 0.83$

What is the probability that two independent customers would recommend the consulting company? Round to four decimal places. (1 point)

This is $P(X = 2)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{2,2}.(0.83)^{2}.(0.17)^{0} = 0.6889$

68.89% probability that two independent customers would recommend the consulting company

What is the probability that one of the two customers would recommend the consulting company [P(A or B)]? Round to four decimal places. (1 point)

This is $P(X = 1)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 1) = C_{2,1}.(0.83)^{1}.(0.17)^{1} = 0.2822$

28.22% probability that one of the two customers would recommend the consulting company.