How do I determine the probability of selecting a card greater than 9 or a black card?
Black cards = 26/52
Cards greater than 9 = 10, jack, queen, king, and depending how you value it, ace
With just the first 4 = (4+4+4+4)/52
The either-or probability is determined by adding the individual probabilities.
4/13
Correct! The probability of selecting a card greater than 9 is 4/13 and the probability of selecting a black card is also 26/52 which simplifies to 1/2. Therefore, the probability of selecting a card that is either greater than 9 or black is 4/13 + 1/2 = 15/26.
To determine the probability of selecting a card greater than 9 or a black card, you need to consider the total number of favorable outcomes and the total number of possible outcomes.
Step 1: Count the number of cards that are greater than 9. In a standard deck of 52 playing cards, there are four suits (hearts, diamonds, clubs, and spades) and each suit contains thirteen cards. Out of these thirteen cards, there are four cards greater than 9 in each suit: 10, Jack, Queen, and King. So, you have a total of 4 x 4 = 16 cards that are greater than 9.
Step 2: Count the number of black cards. In a deck of cards, the spades and clubs are black suits. Each suit contains thirteen cards, so there are 13 black cards.
Step 3: Determine the number of favorable outcomes. In this case, you want to find the probability of selecting a card that is greater than 9 OR a black card. To do this, you add the number of cards greater than 9 (16) to the number of black cards (13), but you need to subtract the number of cards that satisfy both conditions (i.e., both greater than 9 and black). Since there are two black cards greater than 9 (the 10 of spades and the 10 of clubs), you subtract 2 from the total. Therefore, the number of favorable outcomes is 16 + 13 - 2 = 27.
Step 4: Determine the total number of possible outcomes. In a standard deck of 52 playing cards, there are 52 possible outcomes.
Step 5: Calculate the probability. The probability is given by the ratio of favorable outcomes to total possible outcomes. Therefore, the probability of selecting a card greater than 9 or a black card is 27/52, which simplifies to 9/17 (approximately 0.529).
So, the probability of selecting a card greater than 9 or a black card is approximately 0.529, or 9/17.