Answer all questions 1–3 in this document. 1. The manager of a church carnival h

Question

Answer all questions 1–3 in this document. 1. The manager of a church carnival has a choice of two games to include in this year’s carnival. The games are described below. Game 1: This game involves rolling two dice and betting on the sum of the faces. The player will bet $1 and roll the dice. If the total of the roll is a seven (7), the player wins $4. If any other total is rolled, the gambler will lose the dollar bet. Game 2: This game involves the player betting $1 and drawing 1 card from a deck of 52 cards. If the player draws an Ace, they win $4. If they draw a King, they win $3. If they draw a Queen, they win $2. If any other card is drawn, the player will lose the dollar that was bet. Write a short report for the manager evaluating which game is chosen for the carnival this year, assuming the manager wants to maximize the income of the charity. Provide rationale from your calculations in your report. Include the expected value in your report.

Explanation / Answer

Consider the game 1 :

The number of ways by which a sum of 7 of the face value can appear by throwing 2 fair dices is (3,4) , (4,3)

(2,5),(5,2), (1,6), (6,1). All these events are equally likelily so probability getting 7 as sum = 6/36 = 1/6.

So a player is gaining ($4-$1) with probability 1/6

and gaining ($0-$1) = -$1 with probability (1-1/6)=5/6

So expected gain of the player from the game = 3*1/6+ (-1)*5/6= -$1/3. So gain of charity from the game is $1/3.

Now consider game 2.

Probability of coming an ace out of choosing one card is 4/52 = 1/13. Which is the same as the prob of choosing a queen and king.

So the expected gain of the player =

(3+2+1)*1/13+(-1)*10/13 = -$4/13.

So expected gain of the charity is $4/13 which is less than the expected gain of the charity from the 1st game ,$1/3. So manager should include 1st game to maximize income of charity..

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