What is the probability of a student guessing randomly on

pimpinan15t

pimpinan15t

Answered question

2022-02-10

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 & Explanation

Nathalie Frazier

Nathalie Frazier

Beginner2022-02-11Added 15 answers

In total there are 210=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 number 2+5 wrong is the same as number 5+2 wrong). So in all: 2 wrong in (10×9):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:
561024=0.0547=5.47%

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