Question

I am playing a simplified version of the card game, "War," with my brother. We are playing with a subset of the deck, all of the numbered cards 2 through 10 (2:10). There are 4 cards of each number, resulting in 36 total cards in a single pile. First, I turn over a card. Next, he turns over a card. Whoever has the higher card wins and these "used" cards are discarded. If we turn over the same card, we put those cards back into the stack (they are still in the game), and then draw again.

a) To begin the game, we each select a card from our deck without replacement. Assume I have selected an 8. What is the probability that he will win (not tie) on his next draw? Round your answer to three decimal places.

b) Assume that after my previous 8, he drew a 5. I win, and these cards are discarded and we play again with our remaining cards. He draws a 6. What is the probability that I win (not tie) again? Round your answer to two decimal places.

Answer 1

probability that he will win (not tie) on his next draw :

he should take the cards numbered 2 to 7 .

no. of cards he can take to lose =6*4 =24

total cards available = 35

probability =24/35 =0.686

b) now the cards remaining =36-2 =34

he drew 6.

no. of cards 1 can take to win is 7,8,9,10 cards .. total =16

but 8 is discarded so cards = 15

total no. of cards availble =33

probability to win =15/33 =0.45