Find the probability of drawing a diamond card in each of the consecutive draws from a well shuffled pack of cards,if the card drawn is not replaced after the first draw
pr(13/52)(12/51)....until the last card.
To find the probability of drawing a diamond card in each consecutive draw without replacement, we need to consider the number of diamond cards and the total number of cards after each draw.
Let's go through the steps to calculate the probability:
1. Determine the initial number of diamond cards and the total number of cards:
- A standard deck of cards contains 52 cards, and there are 13 diamond cards in total.
2. Calculate the probability of drawing a diamond card on the first draw:
- Since there are 13 diamond cards and 52 total cards, the probability of drawing a diamond card on the first draw is 13/52, which simplifies to 1/4.
3. After drawing a card without replacement, the number of total cards decreases by 1. The number of diamond cards also decreases by 1 since one diamond card has been drawn.
4. Calculate the probability of drawing a diamond card on the second draw:
- After the first draw, there are 51 cards remaining, and the number of diamond cards is reduced to 12.
- Therefore, the probability of drawing a diamond card on the second draw is 12/51.
5. Repeat steps 3 and 4 for consecutive draws:
- After each draw, the total number of cards decreases by 1, and the number of diamond cards decreases by 1.
6. Continue this process until all the diamond cards have been drawn.
It's important to note that the probability of drawing a diamond card in each consecutive draw changes since the total number of cards decreases after each draw.
By following these steps, you can calculate the probability of drawing a diamond card in each consecutive draw without replacement from a well-shuffled pack of cards.