Question

Based on past trends, we have enough reason to believe that 60% of Ha Cafe customers prefer rice and 40% prefer vermicelli. A sample of 5 customers is to be selected. The probability that fewer than 2 prefer rice is

Answer 1

Based on past trends, we have enough reason to believe that 60% of Ha Cafe customers prefer rice and 40% prefer vermicelli.

A sample of 5 customers to be selected.

We have to find the probability that fewer than 2 prefer rice.

Now, given that the probability that a randomly selected person prefers rice is 0.60.

So, if X be the random variable, denoting the number of persons, out of selected 5, who prefer rice, then

X follows binomial distribution with parameters n=5 and p=0.60.

So, the probability mass function of X is given by

Where, r can take any integer value from 0 to 5.

Now, to find

=

=

=

=

So, the probability that fewer than 2 people prefer rice is 0.08704.