Question

A survey found that 35% of callers complain about the service they receive from a call center. Assume that the events of different calls resulting in a complaint are independent. What is the probability that two out of the next five calls produce a complaint?

Answer 1

Answer:

0.336 or 33.6%

Step-by-step explanation:

It follows from the question that the probability of a complaint is 35% = 35/100 = 0.35. Let's call this probability, p.

The probability of no complaint is mutually exclusive of p since both are complements. Let's call this q. Then

q = 1 - p = 1 - 0.35 = 0.65

The distribution is a binomial distribution.

Events of each call are independent.

The probability of 2 calls with complaint out of 5 is

$\binom{5}{2}p^2 \timesq^3=10\times0.35^2\times0.65^3 = 0.336 = 33.6\%$