Math 125 finite and modeling

Question

Draw a single card from a standard deck, find probability of getting an Odd Numbered card

or a Heart.

Answer 1

P(odd or heart) = P(odd) + P(heart) - P(odd & heart)

P(odd) = 5 / 13

P(heart) = 1 / 4

P(odd & heart) = (5/13)(1/4) = 5 / 52

5/13 + 1/4 - 5/52 = ?

Answer 2

Since these two events are not mutually exclusive (an odd card can be a heart as well):

P(Odd or Heart) = P(Odd) + P(Heart) - P(Odd and Heart)

Assuming an Ace is not a numbered card, each suite has 4 odd numbered cards; 3, 5, 7, 9.

4 suites x 4 odd cards each = 16 total odd cards, so P(Odd) is 16/52

There are a total of 13 hearts (Ace → King), so P(Hearts) is 13/52.

But there are 4 cards that are both odd and a heart, so we need to subtract those out to avoid double-counting.

P(Odd or Heart) = 16/52 + 13/52 - 4/52 = 25/52 or around 48%.