A roulette wheel has 38 slots. a gambler will play roulette 50 times, betting a dollar on four numbers each time. if one of these four numbers comes up, she gets the dollar back, together with winnings of $8. if any other number comes up, she loses the dollar. so this bet pays 8 to 1, and there are 4 chances in 38 of winning. her net gain in 50 plays is like the sum of

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Leonard Farley

Mathematics

11 January, 02:43

A roulette wheel has 38 slots. a gambler will play roulette 50 times, betting a dollar on four numbers each time. if one of these four numbers comes up, she gets the dollar back, together with winnings of $8. if any other number comes up, she loses the dollar. so this bet pays 8 to 1, and there are 4 chances in 38 of winning. her net gain in 50 plays is like the sum of

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Kendrick Norman · Answer 1

For 1 play, the chance of gaining $8 is 4/38, while the chance of losing the $1 is 34/38. Therefore, the expected value is ($8) (4/38) + ($-1) (34/38) = $ (-1/19). Over 50 plays, which are mutually independent of each other, we multiply the number of plays by the expected value to get $ (-50/19) = $-2.63.