A card is drawn randomly from a deck of ordinary playing cards. you win $10 if the card is a spade or an ace. what is the probability that you will win the game?

Question

Maddox

Mathematics

24 January, 19:22

A card is drawn randomly from a deck of ordinary playing cards. you win $10 if the card is a spade or an ace. what is the probability that you will win the game?

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Anton Lucero · Answer 1

Since it's an ordinary deck, there are 52 cards in the deck. Assume the deck is fair.

Winning cards are spades and there 13 of those in the deck - the numbers 2 through 10 (9 if them), the three face cards (J, Q, K), and the A.

Winning cards are also aces are there four of them - one for each suit (Hearts, clubs, diamonds, spades)

However the Ace of spades is among both groups so we remove it from the last group to avoid double counting. (You could from the first, but the subtraction is a must)

So there are 13 + 4 - 1 = 16 winning cards out of the deck of 52.

Thus our probability is 16/52.