A classic deck of cards is made up of 52 cards, 26 are black, 26 are red. Each color is split into two suits of 13 cards each (clubs and spades are black and hearts and diamonds are red). Each suit is split into 13 individual cards (Ace, 2-10, Jack, Queen, and King).
If you select a card at random, what is the probability of getting each of the following? (Round to 4 decimal places where possible)
a) The 10 of Diamonds.
b) A Club or a Spade.
c) A number smaller than 10 (counting the ace as a 1).
In each case, the probability is (# matching cards) / (total # cards)
(a) 1/52
(b) 26/52 = 1/2
(c) 36/52 = 9/13
To determine the probability of getting each of the following, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.
a) The 10 of Diamonds:
In a standard deck, there is only one 10 of Diamonds. The total number of cards in the deck is 52. Therefore, the probability of selecting the 10 of Diamonds is 1/52.
b) A Club or a Spade:
There are two suits that are black: clubs and spades. Each suit has 13 cards. So, there are a total of 13 + 13 = 26 black cards. The probability of selecting a Club or a Spade is therefore 26/52, which reduces to 1/2.
c) A number smaller than 10 (counting the Ace as a 1):
There are four suits in a deck, and each suit has cards numbered from Ace (1) to King (13). To find the number of cards numbered smaller than 10, we add up the number of cards from 1 to 9, including the Ace. This gives us 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45. The total number of cards in the deck is 52. So, the probability of selecting a number smaller than 10 is 45/52.
To summarize:
a) The probability of selecting the 10 of Diamonds is 1/52.
b) The probability of selecting a Club or a Spade is 1/2.
c) The probability of selecting a number smaller than 10 is 45/52.