Question

At one large university, freshman accounts 30% of the student body, if a group of 12 students is random chosen by the school news paper to comment on text book prices, what is the probability that at most three of the students are freshme?

Answer 1

Solution

Given that ,

p = 0.30

1 - p = 0.70

n = 12

Using binomial probability formula ,

P(X = x) = ((n! / x! (n - x)!) * px * (1 - p)n - x

P(X 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

= ((12! / 0! (12 - 0)!) * 0.300* (0.70)12 - 0 +  ((12! / 1! (12 - 1)!) * 0.301* (0.70)12 - 1 +  ((12! / 2! (12 - 2)!) * 0.302* (0.70)12 - 2 ​​​​​​​+  ((12! / 3! (12 - 3)!) * 0.303* (0.70)12 - 3 ​​​​​​​

=  0.0138 + 0.0712 + 0.1678 + 0.2397

Probability = 0.4925