Question

You have a standard deck of 52 cards (i.e., 4 aces, 4 twos, 4 threes, …, 4 tens, 4 jacks, 4 queens, and 4 kings) that contains 4 suits (hearts, clubs, spades, and diamonds). We draw one card from the deck. What is the probability that the card is NEITHER a face card (jack, king, or queen) NOR a heart? 27/52

Answer 1

30/52 or 0.5769 or 57.69%

Explanation:

In a standard deck of 52 cards, the number of face cards (F) and the number of hearts (H) is given by:

`F=4+4+4 =12\\H=(52)/(4)=13`

Out of all hearts, three of them are face cards (jack, king, and queen). Therefore, the probability of a card being EITHER a face card or a heart is:

`P(F \cup H) = P(F) +P(H) - P(F \cap H) \\P(F \cup H)=(12+13-3)/(52) =(22)/(52)`

Therefore, the probability of card being NEITHER a face card NOR a heart is:

`P=1-P(F \cup H) \\P=1-(22)/(52)=(30)/(52)\\\\P=0.5769\ or\ 57.69\%`