Monday, September 30, 2013

Without Replacement




A player is dealt 2 cards from a standard deck of 52 cards.
What is the probability of getting a pair of aces?
 
Think about it....obviously this is an experiment "without replacement" because the player was given 2 cards.
To calculate the probability of a pair of aces you use the rules for compound events:
P(ace on first card) = 4/52
(remember,there are 4 aces in the deck)
P(ace on the second card) = 3/51!
(the first card drawn was an ace!)
So the probability of getting 2 aces is:
P(ace,ace) = (4/52)(3/51) = 12/2652 = 1/221!
 


In class I had trouble understanding the difference between Without Replacement and With Replacement. I will explain my learning experiences in another blog about understanding With Replacement. For now I would like to share what, and how I learned to deal with probability problems that deal with Without Replacement. 
So, I found this equation and I found it to be simple and helpful in understanding how exactly Without Replacement works. Using a standard deck of cards is the best way, in my opinion to understand the concept. The equation asked for the probability of getting a pair of aces. By drawing the first card, which is an ace and remember there are 4 aces in a deck, the probability is 4/52. Without Replacement comes into play by not putting that first drawn card back in the deck and simply drawing the next one from a deck of 53 cards.

1 comment:

  1. This concept really threw me off as well. Your equation is really helpful in getting a further understanding to how "without replacement" works. In general, the problems we did with cards all threw me off a bit. I also believe that using a deck of cards and having them in front of you is a great visual to have when figuring out these problems.

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