Solve this problem

Question

Casey ran out of time while taking a multiple-choice test and plans to guess on the last 10 questions. Each question has 4 possible choices, one of which is correct. Let X equal the number of answers Casey correctly guesses in the last 10 questions. Find the probability that she guesses exactly 2 questions correctly.

Answer 1

The number of questions guessed correctly (x) follows a binomial distribution because:

1) You either answer correctly or not

2) Each question is independent

3) There are 10 questions (or trials)

4) The probability of guessing correctly (a success) is constant = 0.25

The probability of getting x successes out of n trials where each trial has probability of success = p:

x n-x

C (p) (1-p)

n x

You just need to apply this formula for n=10 trials, x = 2 successes and p = 0.25