Respuesta :
Answer:
The expectation of the number of correct answers is 17.5
Step-by-step explanation:
For each question, there are only two possible outcomes. Either the student guesses it correctly, or he does not. The probability of a student guessing the answer of a question correctly is independent of other questions. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
In this problem, we have that:
25 questions.
The student know the answer for 10 questions. So for these 10 questions, p = 1.
On the other 25-10 = 15, she will guess, which there is one correct answer out of 2 options(true/false), so p = 1/2 = 0.5. So
[tex]E(X) = 10*1 + 15*0.5 = 17.5[/tex]
The expectation of the number of correct answers is 17.5
