A student is given a truefalse test with 10 questions If she

A student is given a true-false test with 10 questions. If she gets seven or more correct, she passes.
If she is guessing, what is the probability of passing the test?

Please show your work... Thank you!

Solution

Let\'s solve this first in the easy way. As it is true-false, p = .5
Getting 7 right is 1 - P(6 or less correct). From Excel, it is 1 - binomdist(6,10,.5,TRUE)=
1 - 0.828125 = 0.171875

We can also solve it this way. Note that p = 1-p = 1/2.
Thus,
P(7) = C(10,7) (1/2)¹⁰ = 120/1024 = 15/128
P(8) = C(10,8) (1/2)¹⁰ = 45/1024
P(9) = C(10,9) (1/2)¹⁰ = 10/1024 = 5/512

P(10) = C(10,10) (1/2)¹⁰ = 1/1024

P(7) + P(8) + P(9) + P(10) = 15/128 + 45/1024 + 5/512 + 1/1024 = 176/1024 = 11/64 = 0.171875

Note that this checks with the other computation.