Question

A clock tower rings bell every hour. Every hour, it will ring once with probability 1/3 and twice with probability 2/3. The numbers of times the bell rings at different hours are independent.

If we stay on campus for 4 hours (we hear bell on 4 occasions) what is the probability that we hear in total 7 rings?

Answer 1

9.87%

Explanation:

We know that the clock must ring 4 times, but there must be 7 rings. The only way for this to happen is that of the 4 times, 3 that the bell rings 2 times and 1 that rings only once. So it would be:

2 + 2 + 2 + 1 = 7

So the final probability would be the multiplication of these events, therefore:

(2/3) * (2/3) * (2/3) * (1/3) = 0.0987

In other words, the probability is 9.87%