Question

A quiz consists of 10 true or false questions. To pass the quiz a student must answer at least eight questions correctly.

Answer 1

Answer:

The probability of  the student will pass the quiz = .0546

Step-by-step explanation:

Given -

Total no of question = 10

If the student guesses on each question there are two outcomes true of false

the probability  of guesses  question correctly =  $\frac{1}{2}$

the probability  of success is (p) =  $\frac{1}{2}$

the probability  of guesses  question incorrectly = $\frac{1}{2}$

the probability  of failure is (q) = 1- p = $\frac{1}{2}$

If the student guesses on each question he must answered at least 8 question correctly

the probability of  the student will pass the quiz = $P(X\geq8 )$

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

= $\binom{10}{8}(p)^{8}(q)^{10 - 8} + \binom{10}{9}(p)^{9}(q)^{10 - 9} + \binom{10}{10}(p)^{10}(q)^{10 - 10}$

= $\frac{10!}{(2!)(8!)}(\frac{1}{2})^{8}(\frac{1}{2})^{10 - 8} +\frac{10!}{(1!)(9!)} (\frac{1}{2})^{9}(\frac{1}{2})^{10 - 9} + \frac{10!}{(0!)(10!)}(\frac{1}{2})^{10}(\frac{1}{2})^{10 - 10}$

= $45\times\frac{1}{2^{10}} + 10\times\frac{1}{2^{10}} + 1\times\frac{1}{2^{10}}$

= $\frac{56}{2^{10}}$

= .0546