Question

Assume that 2 cards are drawn in succession and without replacement from an ordinary deck of 52 cards. Find the probability that the following occurs.

1 diamond and 1 jack other than the jack of diamonds (in that order) are drawn

Answer 1

52 cards / 4 suites = 13 cards per suite
4 Jacks total ; 1 jack per suite

Chance of drawing a diamond on the first draw: 13/52

Without replacement means once drawn the card is not put back into the pool of cards. So the total cards, suit and type/number all decreases by one.

Chance of drawing one of the 3 non-Diamond Jacks on second draw: 3/51

Chance of drawing Diamond then non-Diamond Jack: (13/52) * (3/51) = 39/2652 = 0.015 (rounded to 1,000s place)