Question

Assume that random guesses are made for ninenine multiple choice questions on an SAT​ test, so that there are nequals=99 ​trials, each with probability of success​ (correct) given by pequals=0.50.5. Find the indicated probability for the number of correct answers. Find the probability that the number x of correct answers is fewer than 44.

Answer 1

The probability that the number of correct answers is 4 is 0.2461.

Explanation:

Let X = number of correct answers.

The probability that an answer is correct is,P (X) = p = 0.50.

The total number of questions is, n = 9.

The event of an answer being correct is independent of the other answers.

The success of each trial is defined as a correct answer with equal probability of success for each trial, i.e. 0.50.

The random variable X follows a Binomial distribution with parameter n = 9 and p = 0.50.

The probability mass function of X is:

`P(X=x)={9\choose x}*0.50^(x)* (1-0.50)^(9-x);\ x=0,1,2,3...`

Compute the value of P (X = 4) as follows:

`P(X=4)={9\choose 4}*(0.50)^(4)* (1-0.50)^(9-4)`

`=126* 0.0625* 0.03125\\=0.24609375\\\approx 0.2461`

Thus, the probability that the number of correct answers is 4 is 0.2461.