10 A deck of playing cards has all the aces and all the numb

10. A deck of playing cards has all the aces and all the number cards removed. The twelve face cards remain. After shuffling, each of three players is dealt a card. (i) What is the probability that the first player gets a king?

Solution

(a)

For first player number of favourable cases =4(4 kings in the pack)

Total number of cases = 12

Probability =4/12=0.33

(b) For second player to have a king there are two cases.

Caes 1. first person gets a king.

Number of favourable outcomes for 2nd person=3

Total number of outcomes =11

P₁=3/11

Case 2: first person doesn\'t get a king

Favourable number of outcomes=4

Total number of outcomes=11

P₂=4/11

Probability(second man gets his first card as king)=Probabilty(first man gets his first card as king)*P₁+Probabilty(first man doesn\'t get his first card as king)*P₂

_{=(4/12)*(3/11)+(8/12)*(4/11)=1/3=0.33}