In the game of roulette a player gives the casino $7 for a bet on the number 5, the player has a 37/38 probability of losing $7 and a 1/38 probability of making a net gain of $245. (The prize is $252 but the players $7 bet is not returned so the net gain is $245.) If a player bets $7 that the outcome is an odd number, the probability of losing $7 is 20/38 and the probability of making a net gain is of $7 is 18/38. (If a player bets $7 on an odd number and wins, the player is given $14 that includes the bet, so the net gain is $7.
a. If a player bets $7 that the outcome is an odd number, what is the players expected value? (Round to the nearest cent)
Confused on this one question in Statistics?
2015-11-15 11:08 pm
回答 (3)
2015-11-15 11:19 pm
expected value=net win(probability of win)-net lost(probability of losing)
ev(5)=245(1/38)-7(37/38)=-$0.368 about -$0.37
ve(o)=7(18/38)-7(20/38)=-$0.368 (the same as before)
The expected value of both bets is to lose 37 cents per bet.
ev(5)=245(1/38)-7(37/38)=-$0.368 about -$0.37
ve(o)=7(18/38)-7(20/38)=-$0.368 (the same as before)
The expected value of both bets is to lose 37 cents per bet.
2015-11-15 11:14 pm
The expected value is just the sum of each outcome's probability times its net gain.
If the player bets on an odd number, then:
20/38 --> net gain is -7 (a loss of the original bet)
18/38 --> net gain is 7 (additional money received over the original bet).
E(X) = (20/38 * -7) + (18/38 * 7)
E(X) ≈ -0.368421
Answer:
The expected value for the player is -0.368 or about about 36.8 cents lost on each play (on average).
If the player bets on an odd number, then:
20/38 --> net gain is -7 (a loss of the original bet)
18/38 --> net gain is 7 (additional money received over the original bet).
E(X) = (20/38 * -7) + (18/38 * 7)
E(X) ≈ -0.368421
Answer:
The expected value for the player is -0.368 or about about 36.8 cents lost on each play (on average).
2015-11-15 11:12 pm
Expected value = ($7 * 18/38) + (-$7 * 20/38).
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