PLEASE HELP ME. This is due tonight and I don\'t know what I\'m doing because I

Question

PLEASE HELP ME. This is due tonight and I don't know what I'm doing because I don't have my book with me. Thanks so much for your help!!

4) A game involves rolling two dice. If the player obtains a sum of 7, she or he is paid $5. Otherwise, the player pays $1. Over time, can the player expect to gain money, lose money, or break even? Determine the player's expected value. Write responses in sentence form. (5 points) 5) A roulette wheel has 38 compartments. Two are numbered 0 and 00 and are colored green. The remaining compartments are numbered 1 through 36; one half are red and one half are black. With each spin of the wheel, a ball falls into one of the compartments. One way of playing this game is to bet on the red or black color. a) What is the probability of obtaining a red number on the spin? (1 point) b) If a player bets $1 on red and wins, the players is paid $1 plus the $1 the player bet ($1 net gain). Otherwise the player loses their $1. What is the expected value of this game? (3 points) c) Is this a fair game? Explain why or why not. Write responses in sentence form. (1 point)

Explanation / Answer

total outcome on pair of dice =6*6 =36

4)a) probability of 7 as sum P(sum =7)=6/36 =1/6 (as thre are 6 outcome in which sum is 7 )

therefore expected value of game =expected win-expected lose =(1/6)*5-(5/6)*1 =0

as expected value of this game is 0 ; therefore it is a fair game and over time player is expected to break even,

5)

a) probability of obtaining a red =18/38 =9/19 (as there are 18 blocks out of 38 are red)

b) expected value of game =expected win-expected lose =(9/19)*1-(10/19)*1 =1/19 =$-0.05

c) as expected value is negative therefore this is not a fair game and over time player is expected to lose money.

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