Question

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?

1. niczorrrr
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.