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

Step-by-step explanation:

Here, the total observation r trials, n = 10

Selected outcomes, r = 5

The probability of getting a right answer, p = $\frac{1}{2} = 0.5$

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,

⇒  $P(5) = \frac{10!}{5!(10-5)!} (0.5)^5 (0.5)^{10-5}$

⇒  $P(5) = 28\times (0.5)^5 (0.5)^5$

⇒  $P(5) = 28\times (0.5)^{10}$

⇒ $P(5) = 28\times 0.0009765625$

⇒ $P(5) = 0.02734375$