Question

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.

Answer 1

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`