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Question
A card is drawn from a pack of playing cards and then another card is drawn without the first being replaced. What is the probability of drawing
- two aces
- two spades
Solution
Number of cards = 52
Number of aces = 4
Number of spades = 13
i. Probability of drawing two aces
`(4"C"_2)/(52"C"_2) = ((4 xx 3)/(2 xx 1))/((52 xx 51)/(2 xx 1)) = (4 xx 3)/(52 xx 51) = 12/2652 = 1/221`
ii. The probability of drawing two spades
`(13"C"_2)/(52"C"_2) = ((13 xx 12)/(2 xx 1))/((52 xx 51)/(2 xx 1)) = (13 xx 12)/(52 xx 51) = 156/2652 = 1/17`
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