A student takes an exam containing 15 true or false questions. if the student guesses, what is the probability that he will get exactly 13 questions right?

Answers

The probability that a student will get exactly 13 questions right is 0.003.

Let E be an event that student gives 13 right answers.

According to the given question.

An exam contain total number of questions is 15.

Now,

The probability that a student gives a right answer, p = 1/2 = 0.5

And, the probability that a student gives a wrong answer, q = 1 – 1/2 = 1/2 = 0.5

Therefore,

The probability that a student will get exactly 13 questions right is given by

⇒ P(E) = C(15, 13) p^(13)q^(15 – 13)

⇒ P(E) = (15!/13!2!)(0.5)^13(0.5)^2

⇒ P(E) = (15(14)/2 ) × ( 0.00012) × 0.25

⇒ P(E) = 105 × 0.00012 × 0.25

⇒ P(E) = 0.00315

Hence, the probability that a student will get exactly 13 questions right is 0.003.

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