The probability of correctly answering 15 questions is 0.88.
What is probability?
A probability is a number that reflects the chance or likelihood that a particular event will occur.
What is the formula for probability?
The formula for the proabability is
[tex]P(E) = \frac{Number\ of \ favorable \ outcomes }{Total\ number\ of\ outcomes}[/tex]
What is binomial probability?
Binomial probability refers to the probability of exactly x successes on n repeated trials in an experiment which has two possible outcomes.
What is the formula for the binomial probability?
The formula for the binomial probability is
[tex]^{n} C_{x} (p)^{x} (q)^{n -x}[/tex]
Where,
x is number of times for a specific outcome within n trials
[tex]^{n} C_{x}[/tex] number of combinations
p is probability of success on a single trial
q is probability of failure on a single trial
n is number of trials
According to the given question.
A test contains total 50 questions with four answer choices.
So,
The probability of getting correct answer = [tex]\frac{1}{4}[/tex]
And, the proability of getting incorrect answer = [tex]1-\frac{1}{4} = \frac{3}{4}[/tex]
Thereofre,
The probability of correctly answering 15 question
[tex]= ^{50} C_{15}( \frac{1}{4}) ^{15} (\frac{3}{4} )^{50-15}[/tex] ( by binomial proability)
[tex]= \frac{50!}{15!35!} (0.25)^{15} (0.75)^{35}[/tex]
[tex]= 0.088[/tex]
Hence, the probability of correctly answering 15 questions is 0.88.
Find out more information about binomial proabability here:
https://brainly.com/question/17011124
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