Math CentralQuandaries & Queries


Question from tabyia, a student:

The common deck of 52 cards has 26 black cards (13 spades and 13 clubs) and 26 red cards (13 hearts and 13 diamonds). Each suit consists of ace, king, queen, jack, ten, nine, eight, seven, six, five, four, three and deuce. 13in all.

A single card is chosen at random. Find the odds against its being a red queen?

How many cards will I have to draw to be absolutely certain that I have drawn three black cards


I'm going to find the odds against drawing a jack.

There are 4 jacks in the deck of 52 cards so the probability of of drawing a jack is 4/52 = 1/13. Hence the probability of not drawing a jack is 1 - (1/13) = 12/13. Therefore, in the long run, if you select a card many times you expect that, on the average, 12 of every 13 times you don't draw a jack and 1 of every 13 times you do draw a jack. Thus the odds against selecting a jack is 12:1. (This is read as 12 to 1.)

Use the same procedure to find the odds against drawing a red queen.


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