Question

Suppose that past history shows that 60% of college students prefer brand c cola. a sample of 5 students is to be selected. based on the binomial probability distribution, the probability that less than 2 prefer brand c is ________.

Answer 1

The probability is 8.7%.

To find P(X<2), we find P(X = 1 or X = 0).  For a binomial distribution, we use the formula
$_nC_r(p)^r(1-p)^{n-r}$

For this problem, p=0.6 and n=5:
$_5C_1(0.6)^1(1-0.6)^4+_5C_0(0.6)^0(1-0.6)^5 \\ \\_5C_1(0.6)(0.4)^4+_5C_0(0.4)^5 \\ \\ \frac{5!}{1!4!}(0.6)(0.4)^4+\frac{5!}{0!5!}(0.4)^5 \\ \\ 5(0.6)(0.4)^4+(0.4)^5 \\ \\0.0768+0.01024 = 0.08704\approx0.087=8.7%$