A student takes a ten-question true-false quiz, but did not study and randomly guesses each answer. Find the probability that the student passes the quiz with a grade of at least 50% of the questions correct.

Step-by-step 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.