Question

In: Statistics and Probability

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

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?

Expert Solution

(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

orchestra answered 1 year ago

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