Answer:

A. To find the probability of drawing a face card or a card with an odd number, you need to determine the number of cards that satisfy either of these conditions and divide by the total number of cards in the deck.

There are 12 face cards (4 jacks, 4 queens, and 4 kings) and 20 cards with an odd number (ace, 3, 5, 7, 9, and jack). However, 4 of these cards (jack, queen, king, and ace) are counted twice, as they are both face cards and odd cards. Therefore, the total number of cards that are either face cards or have an odd number is:

12 + 20 - 4 = 28

So, the probability of drawing a face card or a card with an odd number is:

P(A) = 28/52 = 7/13

B. To find the probability of drawing a black card or a card with a prime number, you need to determine the number of cards that satisfy either of these conditions and divide by the total number of cards in the deck.

There are 26 black cards (13 spades and 13 clubs) and 15 cards with a prime number (2, 3, 5, 7, 11, and 13). However, 6 of these cards (2, 3, 5, 7, 11, and 13) are counted twice, as they are both black and prime cards. Therefore, the total number of cards that are either black cards or have a prime number is:

26 + 15 - 6 = 35

So, the probability of drawing a black card or a card with a prime number is:

P(B) = 35/52 = 5/7