Question

This is about a true-false test. Assume
that 9 questions are answered by guessing.
What is the probability of at least 6 correct answers?_______?

Answer 1

compute the prob you get 6 correct then 7 ,8 then 9...add all together

Answer 2

Easiest way to compute is this:

Answer 3

P(6 or more correct) = P(5 or more correct) - P(exactly 5 correct)

Answer 4

P(5 or more correct) = 1/2, by symmetry.

Answer 5

P(exactly 5 correct) = (9 choose 5) (1/2)^9

Answer 6

9 choose 5 = 9!/(5!4!) = 9(8)(7)(6)/((4)(3)(2)(1)) = 126

Answer 7

So P(6 or more correct) = 1/2 - 126(1/2^9) = 1/2 - 126(1/512) = 1/2 - 126/512 = 1/2 - 63/256 = 65/126.

Answer 8

Or, in decimal form, 0.25390625.

Answer 9

I think you ment to type \[\frac{65}{256}\]

Answer 10

(The next to last line had a typo, the 126 was supposed to be 256, obviously.)

Answer 11

Yes, indeed. And the decimal value had it right.