You have $5 to place a bet in a Las Vegas casino. You decide to bet your $5 on t

Question

You have $5 to place a bet in a Las Vegas casino. You decide to bet your $5 on the number 7 on the roulette table. If you bet $5 on the number 7 in roulette, your probability of losing $5 is 37/38 and the probability of making a net gain of $175 is 1/38. (The prize is $180, including your $5 bet, so the net gain is $175) a.) Find the expected value if you bet $5 on the number 7 b.) Find the mean value if you bet $5 on the number 7 c.) Find the standard deviation value if you bet $5 on the number 7 d.) If you win $50, is that "unusual"? EXPLAIN

Explanation / Answer

a) Expected value = -5x(37/38) + 175x(1/38) = -$0.263

b) Mean = -$0.263

c) Variance = (-5 + 0.263)2x(37/38) + (175 + 0.263)2x(1/38) = 830.194

Standard deviation = sq root(830.194) = 28.813

d) mean + 2 x standard deviation = 57.363

$50 is within 2 standard deviations from mean and hence, it is not unusual to win $50

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