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Chapter 5: Question 81 (page 354)

Use the following information to answer the next three exercises.

The Sky Train from the terminal to the rental–car and long–term parking center is supposed to arrive every eight minutes. The waiting times for the train are known to follow a uniform distribution.

The probability of waiting more than seven minutes given a person has waited more than four minutes is?

a. 0.125

b. 0.25

c. 0.5

d. 0.75

Short Answer

Expert verified

The probability of waiting more than seven minutes given a person has waited more than four minutes is (b)0.25

Step by step solution

01

Defining Conditional Probability

In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.

The formula to be used is :

P(AB)=P(A)P(B)

02

: 

According to provided information, the random variable X for arrival of sky train is following uniform distribution such that:

X~U(0,8)

So, the Probability density function for height will be :

So, the required probability is :

P(x>7x>4)=P(x>7)P(x>4)=(8-7)×18(8-4)×18=14=0.25

Hence, option (b) 0.25is the correct answer.

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