4.133 A Colour Recognition Experiment An experiment is run as follows-the colours red, yellow, and blue are each flashed on a screen for a short period of time. A subject views the colours and is asked to choose which one was flashed for the longest time. The experiment is repeated three times with the same subject.

a. If all the colours were flashed for the same length of time, find the probability distribution for x, the number of times that the subject chose the colour red. Assume that the three choices are independent.

b. Construct the probability histogram for the random variable x.