Cards that fall into more than one of these categories:
2 of diamond, 4 of diamond, 6 of diamond, 8 of diamond, 10 of diamond(both diamond and even number)
3 of diamond, 6 of diamond, 9 of diamond(both diamond and divisible by three)
6 of clubs, 6 of spades, 6 of hearts, 6 of diamond(both even and divisible by three)
Cards that fall into only one of these categories:
1 of diamond, 5 of diamond, 7 of diamond, jack of diamond, queen of diamond, king of diamond(diamonds that aren't even or divisible by three)
Count: 6
2 of clubs, 4 of clubs, 8 of clubs, 10 of clubs, 2 of spades, 4 of spades, 8 of spades, 10 of spades, 2 of hearts, 4 of hearts, 8 of hearts, 10 of hearts(even number cards that aren't diamonds or divisible by three)
Count: 12
3 of clubs, 9 of clubs, 3 of spades, 9 of spades, 3 of hearts, 9 of hearts(cards divisible by three that aren't diamonds or even)
Count: 6
Total: 24
So the probability of <span>drawing a diamond, a card with an even number on it, or a card with a number divisible by three on it, but not a card that falls into more than one of these categories is 24/52 or 6/13.</span>
The probability of a diamond is 13/52 = 1/4 So none of the diamonds can be used for the other 2 restrictions.
The even numbered cards are 2 4 8 10. The 6 cannot be used, because it could come into the next category. Six is divisible by 3. These can come from clubs hearts and spades. So each even number has 3 suits it can come from The number of cards in this category is 3 * 4 = 12 The probability of this occurring is 12/39 = 4/13
The cards divisible by 3 are 3 and 9 [Again you can't use the 6] The Total number of cards are 2*3 = 6 The probability is 6/39 = 2/13
The total probability (without drawing a 6) is 1/4 + 2/13 + 4/13 = 37/52
The two categories where a 6 can turn up are equally likely so choosing the category is 1/2. the probability of a 6 turning up in the first category is 1/2* 3/39 = 3/78 = 1/26
The probability of the 6 turning up in the second category is 1/2 * 3/39 = 3/78 = 1/26 So these two numbers must added into the mix.
