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

`P(5)=(63)/(256)`

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=(1)/(2)`

so, probability getting false question is

`q=(1)/(2)`

the student gets 5 out of 10 questions right

so,

r=5

we can use binomial probability formula

`P(r)=(n!)/(r!(n-r)!) p^rq^(n-r)`

now, we can plug values

`P(5)=(10!)/(5!(10-5)!) ((1)/(2))^5((1)/(2))^(10-5)`

we can simplify it

and we get

`P(5)=(63)/(256)`