Answer: D. 0.377
Step-by-step explanation:
Given : The choices of answers for each question =2
Then , the probability of choosing a correct option : p= 0.5
Total number of question : n=10
Also, to pass the test a student must answer at least 6 questions correctly.
Let x be the random variable that represents the number of questions answered.
Using binomial probability formula, to find the probability of getting success in x trials.
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex]
If a student guesses on each question, then s the probability that the student will pass the test :-
[tex]P(x\geq6)=P(6)+P(7)+P(8)+P(9)+P(10)\\\\=^{10}C_6(0.5)^6(0.5)^4+^{10}C_7(0.5)^7(0.5)^3+^{10}C_8(0.5)^8(0.5)^2+^{10}C_9(0.5)^9(0.5)^1+^{10}C_{10}(0.5)^{10}\\\\=(0.5)^{10}(210+120+45+10+1)\\\\=0.376953125\approx0.377[/tex]
Hence, the probability that the student will pass the test = 0.377
