Question 894332: Thirty tickets numbered 1 to 30 are in a box. Two tickets are drawn together. Find the probability that the
a) sum of the two numbers is odd
b) product of the two numbers is even
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website!
if the sum of the numbers is odd, then one of the numbers has to be even and one of the numbers has to be odd.
the probability of getting an odd first and then an even is 4/8 * 4/7 = 16/56.
the probability of getting an even first and then an odd is 4/8 * 4/7 = 16/56.
the probability of getting one or the other is 16/56 + 16/56 = 32/56 = 4/7.
if the product of 2 numbers is even, they either both have to be even or one of them has to be even and one of them has to be odd.
they cannot both be odd.
the probability of getting an odd first and then an even is 4/8 * 4/7 = 16/56.
the probability of getting an even first and then an odd is 4/8 * 4/7 = 16/56.
the probability of getting an even first and then an even is 4/8 * 3/7 = 12/56.
the total probability is 16/56 + 16/56 + 12/56 = 44/56 = 11/14.
the probability on the second draw is different from the probability on the first draw because you are not replacing the first number when you draw again for the second number.
example:
you start with 4 even and 4 odd for a total of 8.
you remove one even on the first draw.
you are left with 3 even and 4 odd for a total of 7.
if you try to draw an even on the second draw, you will have a choice of 3 out of 7.
if you try to draw an odd on the second draw, you will have a choice of 4 out of 7.
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