A Finite Math student who doesn’t have a clue what’s going on must take a 20 question multiple-choice take home test that has 5 possible answers per question. If this student guesses on every question, what is the probability that they will answer half of the questions correctly?
a) 1 / 20
b) 487 / 187915673
or is it something else?
2007-05-04 03:57:37 · 4 answers · asked by Doug 2 in Science & Mathematics ➔ Mathematics
The probability of answering exactly half of the questions correctly is:
(4/5)^10 * (1/5)^10 * (20!/(10!10!))
(The probability of 10 incorrect answers, times the probability of 10 correct answers, times the number of combinations of 10 correct answers out of 20 questions.)
That's 0.00203.
... which counts as "something else," since it doesn't match either 1/20 or 487/187915673.
2007-05-04 04:05:08 · answer #1 · answered by McFate 7 · 1⤊ 0⤋
2/20
2007-05-04 04:05:39 · answer #2 · answered by yaritza562003 1 · 0⤊ 2⤋
Binomial probability with n=20, p=0.2
Let X=number correct
Pr(X=10) = (20C10) x 0.2^10 x 0.8^10 = 0.0020314
...which is something else
2007-05-04 04:08:05 · answer #3 · answered by joncummins1968 4 · 0⤊ 0⤋
Each question he has a 1/5 chance to get it right, in order to get 10 questions right he would need:
(1/5)¹⁰ = 1/9765625
2007-05-04 04:04:24 · answer #4 · answered by Mαtt 6 · 0⤊ 2⤋