Question

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

Answer 1

Answer:

$P(5)=\frac{63}{256}$

Step-by-step explanation:

we are given

A student randomly guesses on 10 true/false questions

so,

$n=10$

there only true and false

so, probability getting true question is

$p=\frac{1}{2}$

so, probability getting false question is

$q=\frac{1}{2}$

the student gets 5 out of 10 questions right

so,

r=5

we can use binomial probability formula

$P(r)=\frac{n!}{r!(n-r)!} p^rq^{n-r}$

now, we can plug values

$P(5)=\frac{10!}{5!(10-5)!} (\frac{1}{2})^5(\frac{1}{2})^{10-5}$

we can simplify it

and we get

$P(5)=\frac{63}{256}$