If you have a standard deck of 52 cards. You pick one card from the deck and then without putting it back you pick another card . What is the probability that both cards will be 9's
There are 52 cards in a deck, 4 of which are nines.
Initially, the probability of pulling a 9 can be represented by P1, and can be found as:
P1 = Number of 9s/Number of cards
= 4/52
= 1/13
After this, if we pull out a nine (since we want both cards to be nines), then there are 51 cards total and 3 are nines. The probability of pulling out another nine is:
P2 = 3/51
= 1/17
For the probability of both events happening, we multiply these probabilities:
P1* P2
=> (1/13)*(1/17)
=> (1/221)
800words
To find the probability of drawing two 9's without replacement from a standard deck of 52 cards, we need to understand the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
When picking the first card, there are 52 options. After choosing the first card, there are only 51 cards left.
Number of favorable outcomes:
There are 4 cards in the deck that have the value 9 (9 of hearts, 9 of diamonds, 9 of clubs, 9 of spades). After picking the first 9, there will be 3 remaining 9's out of the remaining 51 cards.
So, the probability of drawing a 9 on the first pick is 4/52, and the probability of drawing a 9 on the second pick, given that a 9 was already drawn, is 3/51.
To calculate the probability of both events happening, we multiply the probabilities together:
(4/52) * (3/51) = 12/2652
Simplifying the fraction, we get:
Probability = 1/221
Therefore, the probability of picking two 9's without replacement from a standard deck of 52 cards is 1/221.
To calculate the probability of both cards being 9's, we need to determine the number of favorable outcomes (getting two 9's) and the number of total outcomes.
There are a total of 52 cards in the deck, and when the first card is picked, there are only 51 cards left. Since there are 4 9's in the deck, the probability of picking a 9 on the first draw is 4/52.
After picking the first card, there will be 3 9's left in the deck, since we have already selected one. Out of the remaining 51 cards, there will be a total of 51-1 = 50 cards left that are not 9's.
Therefore, the probability of picking a second 9 is 3/51.
To find the probability of both events happening, we multiply the probabilities of each event together:
(4/52) * (3/51) = 12/2652
Simplifying the fraction, the probability of picking two 9's from a standard deck is:
1/221