Question

A box contains the eleven letters, MISSISSIPPI. Four letters are drawn one by one with replacement and recorded in order. What is the probability that the outcome is pipi?

Answer 1

It is given that a box contains the eleven letters, MISSISSIPPI. It is given that four letters are drawn one by one with replacement and recorded in order. We have to find the probability that the outcome is PIPI.

We know, Probability of any event = (Number of favorable outcomes)/(Total number of possible outcomes)

There are 11 letters and 2 P's. Thus, the probability of the first P in PIPI = 2/11

There are 11 letters and 4 I's. Thus, the probability of the first I in PIPI = 4/11

There are 11 letters and 2 P's. Thus, the probability of the second P in PIPI = 2/11

There are 11 letters and 4 I's. Thus, the probability of the second I in PIPI = 4/11

Thus, the probability of the outcome PIPI = (2/11)*(4/11)*(2/11)*(4/11) = (2*4*2*4)/(11*11*11*11) = 64/14641 = 0.0044(rounded up to four decimal places).

Thus, the probability that the outcome is PIPI = 0.0044 .