Question

Two instructors, Matherton and Staterton. Matherton teaches 16 students and Staterton teaches 19 students

if we pick 10 students. find the following

1. what is the probability that 7 out of the 10 are Matherton
2. what is the probability that at least 9 are Matherton
3. what is the probability that at most 1 is Matherton

Answer 1

Given data,

Probability of being a student of Matherton = 16/35 = 0.4571

Probability of being a student of Staterton = 19/35 = 0.5428

Let x denote the number of students,

We know that binomial distribution is given by,

Where,

n = 10

p = 16/35

1.

= 0.0801

2.

P(X 9) = P(X = 9) + P(X = 10)

= 0.0047 + 0.0004

= 0.0051

3.

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

= 0.0022 + 0.0187

= 0.0209