a student takes up a True or false exam of 10 questions. he is completely unprepared and so he starts guessing randomly. he may toss a coin and use the outcome to determine the guess. compute the probability that he guesses correctly atleast five times.
5/10 = 1/2
binomial distrution
p(5) = C(10,5).5^5 .5^(10-5)
= 252*.5^10 = .246
p(6 ) = C(10,6).5^6 .5^4
= 210 * .5^10 = .205
p(7) = 120 * .5^10 = .117
p(8) = 45 * .5^10 = .044
p(9) = 10 * .5^10 = .01
p(10) = 1 * .5^10 = .001
now add
.623
note that if I split the probability of getting 5 right in half I would get
.123 less
which would be .5 :)
(good check)
Note my check comment
Thank you. But sir I didn't get your 2nd comment about splitting the probability.
You could just as easily lose 5 or more as win five or more.
The triangle is symmetric about that middle point
note C = 252 for point C10,5
then 210 to the left and 210 to the right. The middle point can go either way
Too bad you had an even number of questions :)
That is what misled Ms Sue who assumed symmetry and therefore answer 0.5 immediately.
If you had an odd number there would be a blank in the middle :) and the answer would be 0.50