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Nitella [24]
3 years ago
13

On a multiple-choice test, each question has 4 possible answers. A student does not know

Mathematics
1 answer:
Mnenie [13.5K]3 years ago
6 0

Answer:

1.56% probability that the student gets all three questions right

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the student guesses the answer correctly, or he does not. The probability of the student guessing the answer of a question correctly 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.

Each question has 4 possible answers, one of which is correct.

So p = \frac{1}[4} = 0.25

Three questions.

This means that n = 3

What is the probability that the student gets all three questions right?

This is P(X = 3)

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

P(X = 3) = C_{3,3}.(0.25)^{3}.(0.75)^{0} = 0.0156

1.56% probability that the student gets all three questions right

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