 ## Conditional Probability

Ramon distributes 12 cards into the four piles below:

 Pile A   Pile B    Pile C    Pile D      What is the probability that...
1. a card selected at random is a 7?
2. a card selected at random is from pile B?
3. a card selected from Pile D is a diamond?
4. a card selected from above that is a King was in Pile A or Pile C? 1. The probability a card selected at random is a 7 is P(7) = 3 / 12

2. There are 12 possible cards that may be selected; of these, 4 are in Pile B. Therefore P(card from Pile B) = 4 / 12
3. .

4. There are 5 cards in Pile D. Of these 5 cards, there are 2 diamonds. Therefore, the probability that a card is a diamond given that it is in Pile D is 2 / 5

5. This is an example of conditional probability. For any events (we'll call them A and E), the probability that A will occur given that event E has happened is P(A | E). (This is read "the probability of A, given E.") How do you find P(A | E)?

 P(A | E) = # of ways both A and E can occur = P(A and E) # of ways E can occur P(E)
For this example, we are looking for the probability of getting a diamond given that we have selected a card in Pile D - this is P(diamond | card in Pile D).

 P(diamond | card in Pile E) = P(diamond and in pile D) = 2 / 12 = 2 / 5 ________________ ____ P(in Pile D) 5 / 12
6. To find the probability that a randomly selected King came from Pile A or C we must find...

 P(card is in A or C | King) = # of Kings in A or in C = (# Kings in A) + (# Kings in C) = 3 / 4 ________________ ________________ # of Kings total 4

Think that you have perfected probability? Try the Probability Practice Problems

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