And vs. Or Probability Examples

If you roll a die, what is the probability of it being odd and less than 5?

There 2 numbers that are odd and less than 5: 1 and 3.

If you roll two dice and find their sum, what is the probability of the sum being even or greater than 8?

There are 36 possible combinations, half (18) of which are even; these are shaded in dark blue.  In addition, there are 6 outcomes that are greater than 8 and not even, which are shaded in light blue. 

This makes a total of 18 + 6 = 24 favorable outcomes.

If you draw a card from a deck of cards, what is the probability of it being:

1. a face card and an ace?

2. a 3 and a black card?

3. a face card or a black card?

a. The answer to the first question is a bit tricky: there are no cards that satisfy both conditions, so the probability is 0.

b. The second question is more likely. There are two black suits: spades and clubs. In each of these suits, there is only one 3 card. So there are two black cards with a 3 on them in the entire deck. The probability of drawing a black three is or = 3.8%.

Possible, but not very likely.

c. The third question is a lot more likely. How many face cards are there? There are 3 face cards in each suit (jack, queen, king) so that makes 12 face cards in all.

How many black cards are there? Half of the cards are black so there are 26 black cards. But wait, we already counted 6 of the black cards when we added up the face cards, so that leaves 20 black cards.

There are 32 cards that are a red face card, or a black face card, or a black card. That makes the probability , or 61.5%.