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.
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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