Posted by **Student** on Sunday, March 4, 2012 at 2:02pm.

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?

A. 0.23

B. 0.34

C. 0.66

D. 0.78

- Probability -
**bobpursley**, Sunday, March 4, 2012 at 2:09pm
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

- Probability -
**Student**, Sunday, March 4, 2012 at 2:19pm
How did you get this?

= 6C4 (½)^4 (½)^2 + 6C5 (½)^5 (½)^1 + 6C6 (½)^6 (½)^0

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