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

Answer:

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

Step-by-step 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:

$P(x)=\frac{n!}{x!(n-x)!} *p^{x} *(1-p)^{n-x}$

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)

$P=(\frac{10!}{8!(10-8)!}*0.5^{8}*(0.5)^{10-8})+(\frac{10!}{9!(10-9)!} *0.5^{9} *(0.5)^{10-9})+(\frac{10!}{10!(10-10)!} *0.5^{10} *(0.5)^{10-10})$

P = 0.0439 + 0.0097 + 0.0009

P = 0.0545