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Assume that random guesses are made for six multiple choice questions on an SAT test, so that there are n= 6 trials, each with probability of success (correct) given by p= 0.2. Find the indicated probability for the number of correct answers. Find the probability that the number x of correct answers is fewer than 4.

User Donlelek
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Final answer:

To find the probability of fewer than 4 correct multiple-choice answers, sum the probabilities of 0, 1, 2, and 3 correct answers using the binomial probability formula. This sum represents the probability sought.

Step-by-step explanation:

The student is trying to find the probability that the number x of correct answers is fewer than 4 when guessing on multiple-choice SAT questions. Since each question has a probability of p=0.2 of being correct, we are dealing with a binomial probability problem.

To find the probability of getting fewer than 4 correct answers out of 6, we need to calculate the sum of probabilities for getting 0, 1, 2, or 3 correct answers, which involves using the binomial probability formula P(x) = (nCx)(p^x)(q^(n-x)), where n is the number of trials, p is the probability of success on a single trial, and q is the probability of failure on a single trial (q=1-p).

Applying the formula for each value of x from 0 to 3 and summing those probabilities will give us the desired result.

User Yathish Manjunath
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