Answer:
0.9936 is the probability that the student will fail.
Step-by-step explanation:
We are given the following information:
We treat adult guessing correct answer as a success.
P(guess correct answer) = 0.2
Then the number of correct guesses follows a binomial distribution, where
[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]
where n is the total number of observations, x is the number of success, p is the probability of success.
Now, we are given n = 10
The student needs atleast 6 correct answer to pass the test. We have to calculate the probability that the student will fail.
We have to evaluate:
[tex]P(x < 6) =1 -( P(x = 6)+...+ P(x = 10) )\\\\=1-( \binom{10}{6}(0.2)^6(1-0.2)^4 +...+ \binom{10}{10}(0.2)^{10}(1-0.2)^0)\\\\=1- 0.0064=0.9936[/tex]
0.9936 is the probability that the student will fail.
