One card is selected from a deck of playing cards. Determine the probability of selecting:
a card greater than 9 or a black card.
For 10, jack, queen, king, ace, there are 4 of each. Half of the cards are black, but two each of above 5 values above will also be black. Either-or probability is found by adding the individual probabilities.
20/52 + 26/52 - 10/52 = ?
36/52??
To determine the probability of selecting a card greater than 9 or a black card, we need to first find the number of cards that meet these conditions and then divide it by the total number of cards in the deck.
Step 1: Find the number of cards greater than 9:
There are 4 suits in a deck of playing cards (spades, hearts, diamonds, and clubs), and each suit has 13 cards numbered from 2 to 10, along with 3 face cards (jack, queen, and king). Therefore, there are (13-9) = 4 cards greater than 9 in each suit. Since there are 4 suits, the total number of cards greater than 9 is 4 * 4 = 16.
Step 2: Find the number of black cards:
In a standard deck of 52 playing cards, there are two black suits: clubs and spades. Each suit has 13 cards, so the total number of black cards is 2 * 13 = 26.
Step 3: Find the number of cards that meet both conditions (greater than 9 and black):
To ensure we count each card once, we need to subtract the black cards greater than 9 that we counted twice. There are 2 black suits, each containing 4 cards greater than 9. Therefore, the number of black cards greater than 9 is 2 * 4 = 8.
Step 4: Calculate the probability:
The total number of cards in a deck is 52. So, the probability of selecting a card greater than 9 or a black card is (16 + 26 - 8) / 52 = 34 / 52.
Simplifying the fraction, the probability is 17 / 26.
Therefore, the probability of selecting a card that is greater than 9 or a black card is 17/26.