Question

Assume that random guesses are made for seven multiple choice questions on an SAT​ test, so that there are

equals ​trials, each with probability of success​ (correct) given by

p =0.45

.

Find the indicated probability for the number of correct answers.

Find the probability that the number x of correct answers is fewer than

4

.

Answer 1

Solution :

Number of trials (n) = 12

Probability of success (p) = 0.45

Since, number of trials is finite, probability of success remains constant in each of the trials, and outcomes are independent, therefore we can consider that number of correct answers X follows binomial distribution.

According to binomial probability law, probability of occurrence of exactly x success in n trials is given by,

Where, p is probability of success.

We have to obtain P(X < 4).

We have, n = 12, p = 0.45

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

Using binomial probability law we get,

Hence, the probability that the number x of correct answers is fewer than 4 is 0.1345.

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