Respuesta :
Answer:
2.78% probability that he gets exactly 2 of the twenty questions wrong
Step-by-step explanation:
For each question, there are only two possible outcomes. Either he knows the answer, or he does not. The probability of him knowing the answer for a question 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.
On any question, the student knows the answer with probability .7.
This means that [tex]p = 0.7[/tex]
What is the probability that he gets exactly 2 of the twenty questions wrong, if his performance on different questions is independent
2 of 20 wrong, 20-2 = 18 correctly. So this is P(X = 18).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 18) = C_{20,18}.(0.7)^{18}.(0.3)^{2} = 0.0278[/tex]
2.78% probability that he gets exactly 2 of the twenty questions wrong
