Answer:
[tex]P(5)=\frac{63}{256}[/tex]
Step-by-step explanation:
we are given
A student randomly guesses on 10 true/false questions
so,
[tex]n=10[/tex]
there only true and false
so, probability getting true question is
[tex]p=\frac{1}{2}[/tex]
so, probability getting false question is
[tex]q=\frac{1}{2}[/tex]
the student gets 5 out of 10 questions right
so,
r=5
we can use binomial probability formula
[tex]P(r)=\frac{n!}{r!(n-r)!} p^rq^{n-r}[/tex]
now, we can plug values
[tex]P(5)=\frac{10!}{5!(10-5)!} (\frac{1}{2})^5(\frac{1}{2})^{10-5}[/tex]
we can simplify it
and we get
[tex]P(5)=\frac{63}{256}[/tex]
