You have a standard deck of 52 cards,you pick one card from the deck and them without putting the first card back,you pick a second card.What is the probability both cards will be 9s?
prob(of your event) = (4/52)(3/51) = ...
would the answer be 0.005
D. 0.005
To find the probability of both cards being 9s, we first need to determine the number of favorable outcomes (picking two 9 cards) and the number of possible outcomes (picking any two cards from the deck without replacement).
Let's break it down step by step:
1. Determine the number of 9 cards in the deck:
- Each suit (Spades, Hearts, Diamonds, Clubs) contains one 9 card.
- Thus, there are 4 total 9 cards in the deck.
2. Determine the number of possible outcomes for picking the first card:
- Since there are 52 cards in a deck, the number of possible outcomes is 52.
3. Determine the number of possible outcomes for picking the second card:
- After drawing the first card, there are now 51 cards remaining in the deck.
- Therefore, the number of possible outcomes for the second card is 51.
4. Determine the number of favorable outcomes (both cards being 9s):
- Since there are 4 9 cards in the deck, the number of favorable outcomes for drawing the first 9 is 4.
- After drawing the first 9, there are 3 9 cards remaining in the deck.
- Thus, the number of favorable outcomes for drawing the second 9 is 3.
5. Calculate the probability:
- To find the probability of both cards being 9s, divide the number of favorable outcomes by the number of possible outcomes:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
Probability = (4/52) * (3/51)
Probability = 1/221
Therefore, the probability of picking two 9 cards consecutively without replacement from a standard deck of 52 cards is 1/221.