Question

A test consists of 10 true/false questions. To pass the test a student must answer at least 88 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test? Round to three decimal places.

Answer 1

The probability that the student is going to pass the test is 0.0545

Explanation:

The variable that says the number of correct questions follows a Binomial distribution, because there are n identical and independent events with a probability p of success and a probability 1-p of fail. So, the probability of get x questions correct is:

`P(x)=(n!)/(x!(n-x)!) *p^(x) *(1-p)^(n-x)`

Where n is equal to 10 questions and p is the probability of get a correct answers, so p is equal to 1/2

Then, if the student pass the test with at least 8 questions correct, the probability P of that is:

P = P(8) + P(9) + P(10)

`P=((10!)/(8!(10-8)!)*0.5^(8)*(0.5)^(10-8))+((10!)/(9!(10-9)!) *0.5^(9) *(0.5)^(10-9))+((10!)/(10!(10-10)!) *0.5^(10) *(0.5)^(10-10))`

P = 0.0439 + 0.0097 + 0.0009

P = 0.0545