Question

1) The probability that an individual is left-handed is 12%. In a randomly selected class of 30 students, what is the probability of finding exactly 4 left-handed students?

2) Sixty-five percent of men consider themselves knowledgeable football fans. If 10 men are randomly selected, find the probability that exactly six of them will consider themselves knowledgeable fans.

Answer 1

0.2047

0.2377

Explanation:

1.

What we have here is a binomial distribution

Probability p = 0.12

N = number of students in the class = 30

Probability of finding 4 left handers

P(x = 4) = 30C4 x (0.12)⁴ x (0.88)²⁶

= 27405 x 0.00020736 x 0.03602047835

= 0.2047

2.

This is also a binomial distribution

N = 10 p = 0.65

P(of 6 knowledgeable fans)

= 10C6 x (0.65)⁶ x (0.35)⁴

= 210 x 0.0754189 x 0.01500625

= 0.2377