<h3>
The probability of student passing the quiz with at least 50% of the questions correct is 0.05457.</h3>
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 =
= p = 0.5
Also, the possibility of answering a question wrong =
= 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](https://tex.z-dn.net/?f=%5E%7B10%7DC_8%28p%29%5E8%28q%29%5E2%20%3D%20%5E%7B10%7DC_8%280.5%29%5E8%280.5%29%5E2%20%20%3D%200.0439)
P(answering 9 correct answer) = ![^{10}C_9(p)^9(q)^1 = ^{10}C_9(0.5)^9(0.5)^1 = 0.0097](https://tex.z-dn.net/?f=%5E%7B10%7DC_9%28p%29%5E9%28q%29%5E1%20%3D%20%5E%7B10%7DC_9%280.5%29%5E9%280.5%29%5E1%20%20%3D%200.0097)
P(answering 10 correct answer) = ![^{10}C_{10}(p)^{10}(q)^0 = ^{10}C_{10}(0.5)^{10}(0.5)^0 = 0.00097](https://tex.z-dn.net/?f=%5E%7B10%7DC_%7B10%7D%28p%29%5E%7B10%7D%28q%29%5E0%20%3D%20%5E%7B10%7DC_%7B10%7D%280.5%29%5E%7B10%7D%280.5%29%5E0%20%20%3D%200.00097)
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.