SOLUTION: in one college the second year mathematics students in mathematics have a 50% chance of passing their mathematics examination. Of the 18 second year mathematics students this year,

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Question 994676: in one college the second year mathematics students in mathematics have a 50% chance of passing their mathematics examination. Of the 18 second year mathematics students this year, calculate exactly the probability that they all pass their examination and that exactly one student fails and hence calculate the exactly probability that no more 2 students fail.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
This is a head-tails problem
(0.5)^18=3.815 x 10^(-6)
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That 1 person fails is 18(0.5)^1 (0.5)^17, the 18 being the 18 different ways this can happen.
=6.866 X 10(-5)
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probability 2 fail equals (18C2)(0.5)^2*(0.5)^16=
=153(0.5^18)=5.798 x 10^(-4)
The probability that no more than two fail is the sum of the above, or
0.000003815
0.00006866
0.0005798
=0.0006523