The probability that he will get exactly 6 questions right is 0.0708
What is probability?
"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."
Formula of the probability of an event A is:
P(A) = n(A)/n(S)
where, n(A) is the number of favorable outcomes, n(S) is the total number of events in the sample space.
What is the formula of combination?
"[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]"
What is Binomial distribution formula of probability?
[tex]P=^nC_x\times (p)^x\times (q)^{n-x}[/tex]
where p : probability of success
q: probability of failure
x: number of times for a specific outcome within n trials
n: number of trials
For given question,
A student takes an exam containing 18 true or false questions.
So, n = 18
The probability of success is [tex]p=\frac{1}{2}[/tex]
So, the probability of failure would be,
[tex]q= 1-p\\\\q=1-\frac{1}{2} \\\\q=\frac{1}{2}[/tex]
We need to find the probability that the student will get exactly 6 questions right .
Using Binomial distribution theorem,
[tex]P=^nC_x\times (p)^x\times (q)^{n-x}\\\\P=^{18}C_6\times (\frac{1}{2})^6\times (\frac{1}{2})^{18-6}\\\\P=18564 \times (\frac{1}{2})^6\times (\frac{1}{2})^{12}\\\\P=18564\times \frac{1}{262144}\\\\P=\frac{4641}{65536}\\\\P=0.0708[/tex]
Therefore, the probability that he will get exactly 6 questions right is 0.0708
Learn more about probability here:
brainly.com/question/11234923
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