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Flauer [41]
3 years ago
5

On a multiple-choice test. Abby randomly guesses on all seven questions. Each question

Mathematics
1 answer:
Murrr4er [49]3 years ago
8 0

Answer:

0.173 probability that she gets exactly three questions correct.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either she guesses the correct answer, or she does not. The probability of guessing the correct answer for a question is independent of other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

Seven questions:

This means that n = 7

Each question has four choices.

Abby guesses, which means that p = \frac{1}[4} = 0.25

Find the probability to the nearest thousandth, that Abby gets exactly three questions correct.

This is P(X = 3).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 3) = C_{7,3}.(0.25)^{3}.(0.75)^{4} = 0.173

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