Question

A test consists of 10 true or false questions. To pass the test a student must answer at least eight questions correctly. If the student guesses on each​ question, what is the probability that the student will pass the​ test?

Answer 1

The probability of  student passing the quiz with  at least 50% of the questions correct is 0.05457.

Step-by-step explanation:

Here, the total number of T/F question = 10

The minimum answers needed correctly answered = 8

So, student needs to answer at least 8 questions correctly.

Here, the possibility of answering a question correctly  = $(\frac{1}{2})$   = p = 0.5

Also, the possibility of answering a question wrong  = $(\frac{1}{2})$  = q = 0.5

Now, to pass he needs to answer 8 or more (  8 , 9 or 10) answers correctly.

P(answering 8 correct answer)  = $^{10}C_8(p)^8(q)^2 = ^{10}C_8(0.5)^8(0.5)^2 = 0.0439$

P(answering 9 correct answer)  =  $^{10}C_9(p)^9(q)^1 = ^{10}C_9(0.5)^9(0.5)^1 = 0.0097$

P(answering 10 correct answer)  = $^{10}C_{10}(p)^{10}(q)^0 = ^{10}C_{10}(0.5)^{10}(0.5)^0 = 0.00097$

So, the total Probability   = P(8) + P(9) + P(10)

= (0.0439) + (0.0097) + (0.00097)

= 0.05457

Hence, the probability that the student passes the quiz  with  at least 8 of the questions correct is 0.05457.