Question

If you have already waited for 2 minutes, the probability that you will have to wait at least an additional 3 minutes for a total of more than 5 minutes is:

a) 0.2
b) 0.3
c) 0.4
d) 0.5

Answer 1

The probability of waiting at least an additional 3 minutes for a total of more than 5 minutes after already waiting for 2 minutes is 2/3.

Step-by-step explanation:

To find the probability that you will have to wait at least an additional 3 minutes for a total of more than 5 minutes after already waiting for 2 minutes, we need to understand the distribution of waiting times. Let's assume that the waiting time follows a uniform distribution between 0 and 15 minutes, inclusive.

Since the waiting time is uniformly distributed, the probability density function is a constant. The probability of waiting less than a certain time t is given by the ratio of t to the total range of waiting times (15 minutes in this case).

Therefore, the probability of waiting at least an additional 3 minutes for a total of more than 5 minutes is the same as the probability of waiting more than 5 minutes. Using the uniform distribution, we can calculate this probability as (total range - 5 minutes) / total range = (15 - 5) / 15 = 10 / 15 = 2 / 3.