Respuesta :
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 = [tex]\frac{1}{2}[/tex]
the probability of success is (p) = [tex]\frac{1}{2}[/tex]
the probability of guesses question incorrectly = [tex]\frac{1}{2}[/tex]
the probability of failure is (q) = 1- p = [tex]\frac{1}{2}[/tex]
If the student guesses on each question he must answered at least 8 question correctly
the probability of the student will pass the quiz = [tex]P(X\geq8 )[/tex]
= P(X = 8 ) + P(X = 9) + P(X = 10 )
= [tex]\binom{10}{8}(p)^{8}(q)^{10 - 8} + \binom{10}{9}(p)^{9}(q)^{10 - 9} + \binom{10}{10}(p)^{10}(q)^{10 - 10}[/tex]
= [tex]\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}[/tex]
= [tex]45\times\frac{1}{2^{10}} + 10\times\frac{1}{2^{10}} + 1\times\frac{1}{2^{10}}[/tex]
= [tex]\frac{56}{2^{10}}[/tex]
= .0546
