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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