Question

What is the probability of a student guessing randomly on a test and getting at least 8 out of 10 true and false answers correct?

Answer 1

In total there are `2^10=1024` possible series of right and wrong.

Explanation:

"At least 8 correct" translates to "at most 2 wrong".

0 wrong: can only be done in 1 way

1 wrong: can be done in 10 ways (any of ten questions)

2 wrong: the first wrong may be in 10 places, the second in the nine places left. But since the order of the wrongs doesn't matter, we halve that. (because number2+5 wrong is the same as number5+2 wrong). So in all: 2 wrong in (10x9):2=45 ways.

Total number of ways in which the student may have at most 2 wrongs (=at least 8 right) is:

`1+10+45=56`

On a total of `1024` this gives a probability of:

`56/1024=0.0547=5.47%`