The attached figure shows a point diagram that represents the situation. In this diagram the frequency in which the time between dripping was 1 2 3 4 5 6 7 8 and 9 seconds is observed.
we see that more often, the time between drips is 6 seconds.
However, we want to estimate the probability that the next drip occurs in less than 5 seconds.
The probability that the time between drips will be x seconds is:
P (t = x) = m / n
Where m is the number of times recorded in which the time between dripping was x seconds, and n is the total number of recorded data.
So, the probability that the time between drips is 5 seconds is:
P (t = 5) = 1/17
The probability that the time between drips is less than 5 is:
P (t <5) = P (t = 1) + P (t = 2) + P (t = 3) + P (t = 4)
P (t <5) = 3/17 + 1/17 + 1/17 + 1/17
P (t <5) = 6/17 = 0.3529
P (t <5) = 35.3%
