The mean of a binomial distribution where there are:
n trials with a probability p of ONE sucess in ONE trial,
is given by m = np.
The nearer a number of successes is to the mean of m = np,
the more likely it is to occur.
In this case np = (25)(0.48) = 12.
Therefore the most likely number of successes is 12.
The next most likely is 10, the next is 9, and the least likely is 20.
P(20 sucesses) < P(9 sucesses) < P(10 successes) < P(12 sucesses)
FYI, by actual calculation,
P(12 successes) = 0.15811
P(9 successes) = 0.07897
P(20 successes) = 0.00085
P( 10 sucesses) = 0.11664
The correct answer is, of course, P(12 successes).
Edwin
