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 = [tex]\frac{1}{2} = 0.5[/tex]
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,
[tex]P(r) = n_C_r p^r q^{n-r}[/tex]
Thus, The probability that the student gets 5 out of the 10 questions right,
⇒ [tex]P(5) = \frac{10!}{5!(10-5)!} (0.5)^5 (0.5)^{10-5}[/tex]
⇒ [tex]P(5) = 28\times (0.5)^5 (0.5)^5[/tex]
⇒ [tex]P(5) = 28\times (0.5)^{10}[/tex]
⇒ [tex]P(5) = 28\times 0.0009765625[/tex]
⇒ [tex]P(5) = 0.02734375[/tex]
