Darby guesses the answers to six questions on the math portion of her college entrance exam. Each question is a true or false question. What is the approximate probability that at least 4 of her answers are correct?

Question

A. 0.23
B. 0.34
C. 0.66
D. 0.78

Answer 1

P(at least 4 correct)
= P(4 correct) + P(5 correct) + P(6 correct)
= 6C4 (½)^4 (½)^2 + 6C5 (½)^5 (½)^1 + 6C6 (½)^6 (½)^0
... four correct answers, two incorrect, in any order plus five correct answers, one incorrect, in any order, plus six correct answers, zero incorrect, and only one possible order ...
= 15 (½)^6 + 6 (½)^6 + 1 (½)^6
= (15+6+1) / (2^6)
= 22 / 64
= 11 / 32
= 0.34375

Answer 2

How did you get this?
= 6C4 (½)^4 (½)^2 + 6C5 (½)^5 (½)^1 + 6C6 (½)^6 (½)^0