Respuesta :
Answer:
A.0.236
Step-by-step explanation:
For each question, there are only two possible outcomes. Either Judy guesses it correctly, or she does not. The probability of Judy guessing a question correctly is independent of other questions. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
12 questions
This means that [tex]n = 12[/tex]
5 possible answers, only one of which is correct.
This means that [tex]p = \frac{1}{5} = 0.2[/tex]
If Judy, who forgot to study for the test, guesses on all questions, what is the probability that she will answer exactly 3 questions correctly?
This is P(X = 3).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{12,3}.(0.2)^{3}.(0.8)^{9} = 0.236[/tex]
So the correct answer is:
A.0.236
