Question 233019: Six numbers are chosen at random from the whole numbers between 1 and 16 inclusive, without replacement.
What is the probability that all the numbers are even?
What is the probability that all the numbers are odd?
What is the probability that at least one of the numbers is odd?
Found 2 solutions by edjones, stanbon:
Answer by edjones(8007)   (Show Source):
You can put this solution on YOUR website! 8 of the numbers are even and 8 are odd.
C=n!/((n-r)!r!)
6C8/6C16
=.0035 all are even
=.0035 all are odd
1-.0035=.9965 at least one is odd.
.
Ed
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! Six numbers are chosen at random from the whole numbers between 1 and 16 inclusive, without replacement.
What is the probability that all the numbers are even?
Successful outcomes: 2,4,6,8,10,12,14,16
P(6 even) = (8C6)/16C6 = 28/8008
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What is the probability that all the numbers are odd?
Successful outcomes: 1,3,5,7,9,11,13,15
P(6 odd) = same answer as above.
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What is the probability that at least one of the numbers is odd?
P(at least one odd) = 1 - P(none is odd) = 1-P(all even) = 1-28/8008
= 7980/8008
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Cheers,
Stan H.
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