Question

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

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.