Question

If 2 cards are drawn from a pack one after with over replacement find probability of getting a diamond and a king

Answer 1

1) Cards are drawn without replacement:

    Probability of getting a diamond + king or  king + diamond:
    Here if the first card is a diamond king , then second card is to be one of 3 other kings.  Otherwise, the second card is to be one of 4 kings.
    In the second case, if the first card is diamond king, then the diamond may be one of 12 others. Otherwise the diamond may be one of 13 others.

   Probability: [ 1/52 * 3/51 + 51/52 * 4/51 ] + [ 1/52 * 12/51 + 51/52 * 13/51]
           = (3+204+12+663) / (51*52)

2)  If the cards are drawn with replacement then:
     Probability:  13/52 * 4/52  +  4/52 * 13/52 = 1/26