Question

Roulette: In the game of ro winning. If the metal ball lan player's $5. What is the expce much would you expect to lose? n the game of roulette, a player can place a $5 bet on the number 17 and have a 1/38 probability of the metal ball lands on 17, the player wins S180 (gain of $ 175) Otherwise, the casino takes the What is the expected value of the game to the player? If you played the game 1000 times, how Ichiro's Hit Parade: In the 2004 baseball season, Ichiro Suzuki of the Seattle Mariners set the record for the most hits in a season with a total of 262 hits. In the following probability distribution, the random variable X represents the number of hits Ichiro obtained in a game. (2+3+3+4+4 = 16 points) What is the probability that in a randomly selected game Ichiro got 2 hits? What is the probability that in a randomly selected game Ichiro got more than 1 hit? Compute the Mean, Variance and Standard deviation of the random variable X. Write all formulas and show your calculations in detail | P(x) x*P(x) x² • P(x) 0.1677 0.3354 0.2857 0.1491 0.0373 0.0248

Answer 1

Answer: In the game of roulette, a player can place a $5 bet on the number 17 and have a 1/38 probability of winning. If the metal ball lands on 17, the player win $180. Otherwise, the casino takes the player's $5.

Solution:

P(winning) = 1/38

Profit on winning = $180

P(losing) = 1 - (1/38)

= 37/38

Loss on losing = $5

The expected value of game

= P(winning) * profit + [- P(losing) * loss]

= (1/38 * 180) - (37/38 * 5)

= $4.7368 - $4.8684

= - $0.1316

Therefore, the expected value of game to the player is -$0.13.

If you played the game 1000 times, expect to lose:

Expected loss = 1000 * 0.1316

= $131.6

Therefore, the player would expect to lose about $131.6

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