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A student randomly guesses on 10 true or false questions. Use the binomial model to determine the probability that the student gets 5 out of the 10 questions right. Show all your steps.

User Alysia
by
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1 Answer

4 votes

Answer: 0.02734375

Explanation:

Here, the total observation r trials, n = 10

Selected outcomes, r = 5

The probability of getting a right answer, p =
(1)/(2) = 0.5

Since, the probability of not getting a right answer, q = 1 - p = 1- 0.5 = 0.5

Thus, By the binomial model,

The probability that of getting r outcomes in the n observation,


P(r) = n_C_r p^r q^(n-r)

Thus, The probability that the student gets 5 out of the 10 questions right,


P(5) = (10!)/(5!(10-5)!) (0.5)^5 (0.5)^(10-5)


P(5) = 28* (0.5)^5 (0.5)^5


P(5) = 28* (0.5)^(10)


P(5) = 28* 0.0009765625


P(5) = 0.02734375

User Kimon
by
8.3k points

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