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

1. two aces
2. two spades

Answer 1

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`