Two players A and B are playing a card game They start with

Two players, A and B, are playing a card game. They start with a deck of 26 cards with all clubs and diamonds removed. A will deal 13 cards at random to B and A wins if he gets more aces than B. If both A and B get one ace, the one with the ace of spades wins. They repeat the game 10 times.

(a) Find the probability that A wins 6 times.

(b) If A and B repeat the game 100 times, how many times do you expect A to win?

Solution

A WINS IF HE HAS 2 ACES OR IF HE HAS ACE OF SPADES

PROBABILITY OF GETTING 2 ACES = 2/26

PROBABILITY OG GETTING ACE OF SPADE = 1/2

TOTAL WINNING PROBABILITY = 2/26+1/2 = 0.576

A) PROBABILITY OF WINNING 6 TIMES OUT OF 10 = 10C6*(0.576)^6*(0.424)^4 = 0.247

B)PROBABILITY OF WINING SINGLE GAME = 0.576

SO IF 100 GAMES ARE PLAYED 100*0.576 = 57.6 GAMES CAN BE WON