Question

two cards are drawn in succession from a pack of 52 well-shuffled cards. find the probability that :
1) only the first card is a king
2) first card is a jack of diamonds or a queen 3) at least one card is a picture card
4)not more than one card is a picture card
5) the cards and not of the same suit
6) the second card is not a heart
7) the second card is not a heart given that the first card is a heart
8) the cards are Aces or diamond or boats

Answer 1

Probabilities:
1)  4/52 * 48/51 = 192/2652 = 16/221
     ( explanation : 4- the number of kings, 52- the number of all cards on the pack, 48 - the number of other cards, 51- the number of cards that remain after picking first card)
2) (1/52+4/52) * 51/51 = 5/52 * 1 = 5/52
     ( in brackets are probabilities that 1st card is jack diamond or a queen )
3) 12/52 * 11/51 + 12/52 * 40/51 + 40/52 * 12/51= 91/221 
     ( first is the probability that there are no picture cards, then one picture card: probability 12/52 * 40/51 that 1st is picture card and 40/51 * 12/52 that 2nd is a picture card)
4) 40/52 *39/51 + 12/52 *40/51 + 40/52 * 12/51= 210/221
5) 13/52 * 39/51= 169/884
     ( first is one suit and 2nd is another)
6) 39/52 * 38/51 + 13/52 + 39/51= 19/34
7)13/52 * 39/51 = 13/68  
8) 4/52 * 3/51 + 13/52 * 12/51 + 4/52 * 12/51 + 1/51 =29/663