Question

If 8 minutes have passed since the last customer checked-in, what is the probability that at least another 7 minutes will pass until the next customer checks-in to this hotel?

a) 0.20
b) 0.36
c) 0.45
d) 0.64

Answer 1

To find the probability that at least another 7 minutes will pass until the next customer checks-in to the hotel, we need to find the complement of the probability that less than 7 minutes will pass. Given that 8 minutes have already passed, we can subtract the probability that less than 1 minute will pass from 1 to get the probability that at least 7 minutes will pass.

Step-by-step explanation:

To find the probability that at least another 7 minutes will pass until the next customer checks-in to the hotel, we need to find the complement of the probability that less than 7 minutes will pass. Given that 8 minutes have already passed, we can subtract the probability that less than 1 minute will pass from 1 to get the probability that at least 7 minutes will pass.

The probability that it takes less than 1 minute for the next customer to arrive can be found using the given information: one customer arrives every two minutes on average. Therefore, the probability of waiting less than 1 minute is 1/2.

Subtracting 1/2 from 1, we get the probability that at least 7 minutes will pass is 1 - 1/2 = 1/2.