SOLUTION: I have a problem regarding probability. Here it is... It is known that 53% of graduating students are boys. Three grads are chosen at random. Given that at least two of the thre

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Question 111560: I have a problem regarding probability. Here it is...
It is known that 53% of graduating students are boys. Three grads are chosen at random. Given that at least two of the three grads are boys, determine the probability that all three of the grads are boys.
I believe the answer is either 0.14887 or 53%.
Thanks for any help.
Answer by edjones(8007) (Show Source):
You can put this solution on YOUR website!
.53^3=.148877 Prob all 3 are boys
.53^2*.47*3=.396069 prob 2/3 are boys
.53*.47^2*3=.351231 prob 2/3 are girls
.47^3=.103823 all girls
If all 4 probabilities above are added the sum = 1
The reason for the 3 being multiplied in the 2nd and 3rd equations is because
nCr=3C2=3 and 3C1=3
We are only allowed the probability of all boys or 2/3 boys so we add the 1st two probabilities.
.148877+.396069=.544946 our universe (denominator)
.
.148877/.544946=.273196 prob that all three are boys given that, at least 2/3 are boys.
Ed