You are playing a card game with a full deck of 52 cards. You win if you draw a red card that is a multiple of 5. What are your chances of winning on your first draw?
How many red cards are there that are a multiple of 5 ?
So that number "over" 52
To calculate the chances of winning on the first draw, we need to determine the number of favorable outcomes (red cards that are multiples of 5) and the total number of possible outcomes.
1. Number of favorable outcomes:
- There are a total of 52 cards in the deck.
- Half of them are red, so there are 26 red cards.
- Out of these 26 red cards, the multiples of 5 are 5, 10, 15, 20, 25, and 30 (6 cards in total).
2. Total number of possible outcomes:
- There are still 52 cards in the deck.
3. Calculating the chances of winning:
- The probability of winning on the first draw is given by the favorable outcomes divided by the total outcomes.
- Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
- Probability = 6/52
- Simplifying, we get Probability = 3/26
Therefore, your chances of winning on your first draw are 3 out of 26, or approximately 11.54%.
To find the probability of winning on your first draw, we need to determine the number of favorable outcomes (red cards that are multiples of 5) and the number of possible outcomes (total number of cards).
Step 1: Determine the number of favorable outcomes.
In a deck of 52 cards, there are 26 red cards (hearts and diamonds) since half of the deck is red. To find the number of red cards that are multiples of 5, we need to identify which cards meet this condition. These cards are: 5 of hearts, 5 of diamonds, 10 of hearts, 10 of diamonds, 15 of hearts, 15 of diamonds, 20 of hearts, 20 of diamonds, 25 of hearts, 25 of diamonds, 30 of hearts, 30 of diamonds, 35 of hearts, 35 of diamonds, 40 of hearts, 40 of diamonds, 45 of hearts, 45 of diamonds, and 50 of hearts, which makes a total of 18 favorable outcomes.
Step 2: Determine the number of possible outcomes.
In a standard 52-card deck, there are 52 cards total.
Step 3: Calculate the probability of winning on your first draw.
The probability is determined by dividing the number of favorable outcomes by the number of possible outcomes.
Probability of winning on first draw = (Number of favorable outcomes) / (Number of possible outcomes)
Probability of winning on first draw = 18 / 52
Simplifying the fraction, we get:
Probability of winning on first draw ≈ 0.3461 or 34.61%
Therefore, your chances of winning on your first draw in this card game are approximately 34.61%.