What is the probability that if you draw a card from a standard deck of cards that it is a card of Diamonds or an 8 ?
prob(diamonds) = 1/4
prob(an 8) = 4/52 = 1/13
prob(the 8 of diamonds) = 1/52
prob(an 8 or a diamond) = 1/4 + 1/13 + 1/52
= 13/52 + 4/52 - 1/52 = 15/52 = 4/13
4/52
To calculate the probability of drawing a card that is either a Diamond or an 8, we need to determine the number of favorable outcomes and the total number of possible outcomes.
There are 13 cards of each suit in a standard deck, and Diamonds is one of the four suits. Therefore, there are a total of 13 Diamond cards in the deck.
Additionally, there are four 8's in the deck (one for each suit).
To find the total number of favorable outcomes, we need to add the number of Diamond cards and the number of 8's: 13 + 4 = 17.
The total number of cards in a standard deck is 52.
To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes: 17/52 ≈ 0.327.
Therefore, the probability of drawing a card that is either a Diamond or an 8 is approximately 0.327, or 32.7%.
To find the probability of drawing a card that is either a Diamond or an 8 from a standard deck of cards, we need to know the total number of favorable outcomes (cards that are Diamonds or 8s) and the total number of possible outcomes (all cards in the deck).
Step 1: Determine the number of favorable outcomes:
- There are 13 Diamonds in a standard deck of cards since each suit (Hearts, Diamonds, Clubs, Spades) contains 13 cards of different ranks.
- There are 4 8s in a standard deck of cards since the ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) have 4 cards of each rank.
So, the number of favorable outcomes (cards that are Diamonds or 8s) is 13 (Diamonds) + 4 (8s) = 17.
Step 2: Determine the number of possible outcomes:
- A standard deck of cards has 52 cards because there are 4 suits (Diamonds, Hearts, Clubs, Spades), and each suit has 13 different ranks.
So, the number of possible outcomes (all cards in the deck) is 52.
Step 3: Calculate the probability:
- Probability is calculated by taking the number of favorable outcomes divided by the number of possible outcomes.
Therefore, the probability of drawing a card that is a Diamond or an 8 is:
17 (favorable outcomes) / 52 (possible outcomes) ≈ 0.327.
Hence, the probability is approximately 0.327 or 32.7%.