Question

Suppose an operator handles 10 calls. What is the probability that none of the 10 calls result in a reservation?

Answer 1

Question:

Approximately 30% of the calls to an airline reservation phone line result in a reservation being made.  Suppose that an operator handles 10 calls. What is the probability that none of the 10 calls result in a reservation?

Answer:

$Probability = 0.028$

Step-by-step explanation:

Given

Represent probability of reservation with p and Number of calls  with n

$n= 10$

$p = 30\%$

First, we need to convert p to decimal

$p = \frac{30}{100}$

$p = 0.30$

In probability; opposite probability add up to 1;

In other words,

$p + q = 1$

Where q represents probability of no reservation

Substitute 0.30 for p

$0.30 + q = 1$

$q = 1 - 0.30$

$q = 0.70$

The probability that out of the 10 calls, no reservation is made is calculated as;

$Probability = q^n$

$Probability = 0.70^{10}$

$Probability = 0.0282475249$

$Probability = 0.028$  (Approximated)