SOLUTION: You pick two cards from a standard deck of 52 cards. What is the probability you choose a 9 and then an ace if you do not replace the first card. Please explain step by step :)

Question 988419: You pick two cards from a standard deck of 52 cards. What is the probability you choose a 9 and then an ace if you do not replace the first card.
Please explain step by step :)
Found 2 solutions by rfer, solver91311:
Answer by rfer(16322) (Show Source): You can put this solution on YOUR website!
4/52*4/51=16/2652=4/663
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The probability of anything is the number of ways the event can happen that you would consider a success divided by the number of ways that it can happen at all. To get the 9, of which there are 4 in the deck of 52, you have a 4/52 or 1/13 chance. Then, since you didn't replace the first card, you want, on the second draw, to select one of four aces out of what is now 51 cards.

Since you calculated the second probability based on the assumption that the first draw was successful, the two draws become independent events. Hence, the overall probability is the product of the two probabilities.

John

My calculator said it, I believe it, that settles it

RELATED QUESTIONS
What are the odds that you will pick an ace from a standard deck of 52 cards? (answered by josmiceli)
how do you find the answer to the problem two cards are drawn from a standard 52 deck... (answered by rfer)
You choose at random two cards from a standard deck of 52 cards. What is the probability (answered by Alan3354)
You have a standard deck of 52 cards you pick one card from the deck and then without... (answered by ewatrrr)
you are dealt five cards from a standard deck of 52 cards. What is the probability of... (answered by stanbon)
You are dealt five cards from a standard deck of 52 cards. What is the probability of... (answered by JulietG)
In a standard deck of playing cards, there are 52 total cards. Half of the cards are red (answered by Edwin McCravy)
You take the four Aces, four 2's, and four 3's from a standard deck of 52 cards, forming... (answered by ikleyn)
If you draw 5 cards from a standard 52 card deck, what is the probability of getting 5... (answered by stanbon)