Question

1. There are 65 students, 35 females and 30 males in a class. How many ways to choose 3 students so that 1 of them is male?

2. A student is writing a multiple choice test with 20 questions. Each question has 4 possible answers. The student will randomly choose one of the 4 answers for each question. What is the probability the student answers at least 2 questions correctly?

(please answer questions step by step)

Answer 1

1. total 65 students

male = 30

female = 35

TO find : ways to choose 3 students such that 1 of them is male

Male can be chosen in ₃₀C₁ ways

Female cane be chosen in ₃₅C₂ ways

Total number of ways = ₃₀C₁ * ₃₅C_{2 =} 30 * 595 = 17850 ways

ways to choose 3 students such that 1 of them is male = 17850 ways

2.

Total number of questions = 20

Each question has 4 options out of which one is correct, so probability of correct answer = 1/4 = 0.25

To find : Probability that the student answers at least two questions correctly

P(x is at least 2 ) = P (2) + P(3) +P(4) ......P(20)

To find the above we can find the probability of 0 and 1 correct answer and subtract from 1

P(x is at least 2 ) = 1- [0.00317 + 0.02114] = 0.97569