Question 1179724: in a box of 100 chocolate bars, there are 20 Kit Kat, 30 smarties, 10 coffees crisps and 40 aeros. You draw a chocolate bars and replace it, what is the probability of drawing atleast 3 smarties
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52786)   (Show Source):
You can put this solution on YOUR website! .
in a box of 100 chocolate bars, there are 20 Kit Kat, 30 smarties, 10 coffees crisps and 40 aeros.
You draw a chocolate bars and replace it, what is the probability of drawing atleast 3 smarties
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As it is worded, printed, posted and presented, the problem is posed INCORRECTLY.
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@Theo incorrectly interprets and solves the problem.
In order for the problem be posed correctly, the number of trials should be given in the condition -
BUT IT IS NOT GIVEN IN THE PROBLEM.
Therefore, the "solution" by @Theo is a FICTION, is INCORRECT, is FALSE and EMPTY.
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! the probability of getting at lest 3 is equal to 1 minus the probability of getting less than 3.
the probability of getting less than 3 is equal to the probability of getting 0 or 1 or 2 only.
this is a binomial problem where p(x) = c(n,x) * p^x * q^(n-x).
n = 100
x = 0 or 1 or 2
c(n,x) = n! / (x! * (n-x)!
specifically, ...
p(one smartie) = 30/100 = 3/10 = .3
p(anything but one smartie) = 1 - .3 = .7
since you are replacing the chocolate bar each time, the probability remains the same for each draw.
p(0) = .3^0 * .7^(100 - 0) * c(100,0) = 3.23447651 * 10^-16
p(1) = .3^1 * .7^(100 - 1) * c(100,1) = 1.38620422 * 10^-14
p(2) = .3^2 * .7^(100 - 2) * c(100,2) = 2.94073323 * 10^-13
the total probability of getting less than 3 is equal to 3.08258813 * 10^-13.
the total probability of getting at least 3 is 1 minus that.
my calculator couldn't handle it, so i went to excel.
this is what i got.
p(less than 3) = 3.08258813312174 * 10^-13
p(3 or greater) = 1 minus p(less than 3) = 9.99999999999686 * 10^-1
i went a little further.
the best excel could give me is:
p(3 or greater) = 0.999999999999692
i resorted to calculating it manually and the best that i could do is:
p(3 or greater) = 0.999999999999601741186687826
it's kind of like a moot point.
if you round your answer to anything less than 12 digits, the answer is p(3 or greater) = 1.
sticking to the answer that the calculator gave me, i would go with p(3 or greater) = 1 or p(3 or greater) = 1 minus p (less than 3) = 1 minus 3.08258813 * 10^-13.
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