Problem 1144

Two cards are drawn without replacement from an ordinary deck, find the probability that the second id a club, given that the first is not a club.




After the first card is draw from the deck, 51 cards are left to choose from.

This partial deck of 51 cards is the reduced sample space used to calculate the probability when the second card is drawn.

After the first card (not a club) is drawn from the deck, 12 are left fall into the category ‘a club’.

The probability that the second is a club, given the  first is not a club is \frac{13}{51}. In lowest terms, P(a club | not a club ) = \frac{13}{51}.



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