Question

Suppose that it is past noon on a delivery day, The probability that a person must wait at least one and half more hours is;

a.$\frac{1}{4}$

b. $\frac{1}{2}$

c. $\frac{3}{4}$

d.$\frac{3}{8}$

Short answer

The probability that a person must wait at least one and half more hours is: $\frac{1}{4}$.

Therefore, option "a" is the correct answer.

Step-by-step solution

Given information

Given in the question that, the time to wait a particular rural bus is distributed as uniformly from$0$to$75$minutes.

Explanation 

According to the information, we observed that the given distribution will follow the uniform distribution as follow:

$X~U(0,75)$

On a delivery day, the waiting time will be 12 P.M to 2. P.M.

Therefore, the probability that a person must wit one and half more hours is given as:

$P(X>1.5)=1-(X\le 1.5)$

$=1-\left[\frac{1.5-0}{2}\right]$

$=\frac{5}{20}$

$=\frac{1}{4}$

Therefore, option 'a' is the correct answer.