The probability of student passing the quiz with at least 50% of the questions correct is 0.62267.
Explanation:
Here, the total number of T/F question = 10
The minimum answers needed correctly answered = 50%
Now, 50% of 10 = 5 questions
So, student needs to answer at least 5 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 5 or more ( = 5, 6 , 7 , 8 , 9 or 10) answers correctly.
P(answering 5 correct answer) =

P(answering 6 correct answer) =

P(answering 7 correct answer) =

P(answering 8 correct answer) =

P(answering 9 correct answer) =

P(answering 10 correct answer) =

So, the total Probability
= (0.246) + (0.2050)+ (0.1171) +(0.0439) + (0.0097) + (0.00097)
= 0.62267 ≈ 62.2 %
Hence, the probability that the student passes the quiz with a grade of at least 50% of the questions correct is 0.62267.