Assume that random guesses are made for 8 multiple choice questions on an sat test, so that there are n=9 trials, each with probability of success (correct) given by p=0.6. find the indicated probability for the number of correct answers. find the probability that the number x of correct answers is fewer than 4.

Probabilities are used to determine the chances of an event

The probability that the number of correct answers is fewer than 4 is 0.0994

The given parameters are:

The probability is a binomial probability, and it is calculated using:

Fewer than 4 means: x = 0, 1, 2 and 3

So, we have:

This gives

Using a calculator,

Approximate

Hence, the probability that the number of correct answers is fewer than 4 is 0.0994

Read more about binomial probabilities at:

link

Step-by-step explanation:

If we call x the number of correct questions obtained in the 9 attempts, then:

x is a discrete random variable that can be modeled by a binomial probability distribution p, with n = 9 trials.

So, the p of x successes has the following formula.

Where:

n = 9

p = 0.6

We are looking for P(x<4)

By definition:

Then:

yes because there is exactly one y value for every x value

for function there can't be more than one value for every x value