Choosing From Cards
Level
1
There are 6 cards with the numbers 1, 2, 3, 4, 5 and 6 written on them. The cards were turned over and shuffled.
You take 3 of the 6 cards.
Is it more likely that the sum of the numbers chosen are odd or even?
Between the sums of 6 and 15, 10 is most likely to come up, so even is more likely
Both are as likely
This is by luck
It is more likely for odds and evens to be chosen, so odd is more likely
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1 solution
You choose 3 out of 6 cards. The number of possible ways is 6x5x4/1x2x3= 20.
Now, assume the sum is odd. This can happen if all 3 cards are odd, or if 2 are even and 1 is odd.
There are only 3 odd cards in this deck of 6 cards, so the chances all 3 cards are odd is 1/20.
With the other case, the chances is (3x2/1x2 times 3)/20, which is 9/20.
The sum of the chances in both cases is 10/20, which is 1/2.
Hence, the chances of getting odd or even is the same.