A game is played by choosing 2 cards randomly from a deck of cards.
Everytime you choose 2 cards that are face cards or 2 cards that are consecutive (i.e. 4 and 5, Jack and Queen), you win the game. If you recieve $2.00 everytime you win the game, determine the expected amount of winnings after 100 games.
I am going to work this out assuming that Im working with the following; King, Queen, Jack, 10, 9, 8, 7, 6, 5, 4, 3, 2, and Ace
Thats 13 cards per suit; Diamonds, Spades, Clubs and Hearts
a total of 52 cards
First lets calculate the probability of drawing two consecutive cards from one suite;
you win only if the two cards are consecutive;
= 13(c2) = 13 x 12 / 2 = 78
so ...no of ways this can happen is ( n -1 ) = 13- 1 = 12
probability for win = 12 /78 per suit
For 100 games number of wins;
= 100 x 12 / 78 = $15.38 x 2$ per win = $30.76
to get the probability of the deck divide by 4
$30.76 / 4 = $7.69
Hope this helps
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