Question

What is the probability that the lecture continues for at least 105 seconds beyond the end of the hour? (Round your answer to four decimal places.)

a) 0.105
b) 0.285
c) 0.645
d) 0.395

Answer 1

The probability that the lecture continues for at least 105 seconds beyond the end of the hourb is b) 0.285.

Step-by-step explanation:

To calculate the probability that the lecture continues for at least 105 seconds beyond the end of the hour, we need to use the fact that the lecture ends at the end of the hour, which is 60 minutes. Since the lecture continues for at least 105 seconds beyond the end of the hour, we know that it must continue for at least 105 seconds after the hour ends.

Let’s assume that the lecture ends at the end of the hour, which is 60 minutes. Therefore, the total time of the lecture is 60 + 105 = 165 minutes.

Now, we need to find the probability that the lecture continues for at least 105 seconds beyond the end of the hour. To do this, we can use the formula for the probability of an event occurring:

P(event) = number of favorable outcomes / total number of outcomes

In this case, the number of favorable outcomes is the time that the lecture continues beyond the end of the hour, which is 105 seconds. The total number of outcomes is the total time of the lecture, which is 165 minutes.

Therefore, the probability that the lecture continues for at least 105 seconds beyond the end of the hour is:

P(lecture continues for at least 105 seconds) = 105/165 = 0.285

So, the answer is b) 0.285.