Probability:You are given a deck of fifty two cards which have printed on them a pair of symbols

Question

You are given a deck of fifty two cards which have printed on them a pair of symbols: an integer between 1 and 13, followed by one of the letters “S,” “H,” “D,” or “C,” There are 4 × 13 = 52 such possible combinations, and you may assume that you have one of each type, handed to you face down.

(a) Suppose the cards are randomly distributed and you turn them over one at a time. What is the average cost (i.e. number of cards turned over) of finding the card [11,H]?

(b) Suppose you know that the first thirteen cards have one of the letters “H” or “D” on them, but otherwise all cards are randomly distributed. Now what is the average cost of finding [11,H]?

Answer 1

(a)[11,H] it is a perticular card

So, min no of turn to get it could be first turn i.e.=1

      max no. of turn to get it could be the last turn i.e.=52

Here we will take avg turn i.e. 1+52/2 =26.5

(b)If first 13 cards have H in all then avg. turn will be 13+1/2=7

    if first 13 cards have D in all then avg. turn will be 39+1/2 =20

Comments

i think average is asked. which should be ( best case + worst case )/2

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But they told number of cards turn over, not avg no of cards turn over. thats why I have taken max no of cards turn over. ok edited,