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VMariaS [17]
3 years ago
11

A student takes an exam containing 1818 true or false questions. If the student guesses, what is the probability that he will ge

t exactly 66 questions right? Round your answer to four decimal places.
Mathematics
2 answers:
creativ13 [48]3 years ago
8 0

Probability

p=66×100/1818=3.6303630363%

After rounding to 4 decimals:

p=3.6304%

Juli2301 [7.4K]3 years ago
7 0

Answer:

0.0708 = 7.08% probability that he will get exactly 6 questions right.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the student guesses the correct answer, or he guesses the wrong answer. The probability of guessing the correct answer in a question is independent from 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.

18 questions

This means that n = 18

True or false, guessed.

Each question has two possible answers, so p = \frac{1}{2} = 0.5

If the student guesses, what is the probability that he will get exactly 6 questions right?

This is P(X = 6)

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

P(X = 6) = C_{18,6}.(0.5)^{6}.(0.5)^{12} = 0.0708

0.0708 = 7.08% probability that he will get exactly 6 questions right.

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