Answer:
12. The probability of selecting a spade or a six: There are 13 spades and four sixes in a standard deck of 52 cards. However, one of the cards (the six of spades) is counted twice. Therefore, the total number of cards that are either spades or sixes is 13 + 4 - 1 = 16. So, the probability of selecting a spade or a six is 16/52 = 4/13.
13. The probability of selecting a black card or a jack: There are 26 black cards and four jacks in a standard deck of 52 cards. However, two of the cards (the jack of clubs and the jack of spades) are counted twice. Therefore, the total number of cards that are either black cards or jacks is 26 + 4 - 2 = 28. So, the probability of selecting a black card or a jack is 28/52 = 7/13.
14. The probability of selecting a seven or a face card: There are four sevens and 12 face cards (which include jacks, queens, and kings) in a standard deck of 52 cards. However, three of the cards (the jack, queen, and king of hearts) are counted twice. Therefore, the total number of cards that are either sevens or face cards is 4 + 12 - 3 = 13. So, the probability of selecting a seven or a face card is 13/52 = 1/4.
15. The probability of selecting a face card or a queen: There are 12 face cards and four queens in a standard deck of 52 cards. However, one of the cards (the queen of hearts) is counted twice. Therefore, the total number of cards that are either face cards or queens is 12 + 4 - 1 = 15. So, the probability of selecting a face card or a queen is 15/52 = 15/52.
16. The probability of selecting a four or a king: There are four fours and four kings in a standard deck of 52 cards. However, one of the cards (the king of hearts) is counted twice. Therefore, the total number of cards that are either fours or kings is 4 + 4 - 1 = 7. So, the probability of selecting a four or a king is 7/52 = 1/7.