30 of all students are over 25 years old at a certain univer

30% of all students are over 25 years old at a certain university. If five students at the university are randomly selected. What is the probability that at least one student is over 25 years old. Write the probability as a proportion rounded to 3 decimal places.

Solution

This is binomial distribution problem

p = proportion of students over 25years = 30% =0.3

n = 5

P(X >=1) = 1 - P(X <1)

= 1- P(X=0)

= 1 - 5C0 * 0.3^0 * 0.7^5

= 0.832