Question

A survey of Lakeview High School students found that 72% of the students had eaten breakfast that morning. If two students are chosen at random from a group of 100 students, what is the probability that at least one of them did not eat breakfast that morning?

Answer 1

4.26 * 10^-12

Explanation:

Usibg the binomial probability relation :

P(x =x) = nCx * p^x * q^(n-x)

Probability of success = probability of not eating = 1 - 0.72 = 0.28

p = 0.28

q = 1 - p = 0.72

Probability that atleast one out of 2 chosen did not eat breakfast :

P(x ≥ 1) = p(x = 1) + p(x = 2)

P(x ≥ 1) = (100C1 * 0.28^1 * 0.72^99) + (100C2 * 0.28^2 * 0.72^98)

= 4.26 * 10^-12