Question

Mimi plans to make a random guess at 5 true-or-false questions.

a. Assume random number X is the number of correct answers Mimi gets. As we know, X follows a binomial distribution. What is n (the number of trials), p (probability of success in each trial) and q (probability of failure in each trial)?

b. How many correct answers can she expect to get?

Mimi plans to make a random guess at a test containing 5 true-or-false questions.

a. Mimi plans to make a random guess at 5 true-or-false questions. What is the probability that Mimi will pass the test by random guess?

b. What function can be used to find the probability?

Answer 1

(a) Number of trials, n = 5

Probability of success in each trial, p = 0.5 (since any one option true or false can be correct both of which has probability of 0.5)

Probability of failure in each trial, q = 1 - p = 0.5

(b) Number of correct answers that she can expect to get = np = 2.5

Here, the criteria of passing the test is not given

(a)

Case 1: When all the answers need to be correct to pass the test, the probability of passing the test by random guess = = 1/32

Case 2: When atleast 4 out of 5 answers need to be correct, the required probability = = 6/32

Case 3: When atleast 3 out of 5 answers need to be correct, the required probability = = 1/2

Case 2: When atleast 2 out of 5 answers need to be correct, the required probability =

= 26/32

(b) Binomial distribution can be used

P(X = x) = , x = 0,1,2,....,n