A modified roulette wheel contains 38 numbers, of which 18 are red,18 are black,

Question

A modified roulette wheel contains 38 numbers, of which 18 are red,18 are black, and 2 are green. When the roulette wheel is spun, the ball is equally likely to land on any of the 38 numbers. For a bet on black, the house pays 1 to 2 odds. What should the odds actually be to make the bet fair? (Hint: To make the bet fair, the odds paid by the house should be the odds against the ball landing on black.)

The odds, in simplified form, should actually be nothing to nothing to make the bet fair. (Type whole numbers.)

Explanation / Answer

P(Black) = 18/38 = 9/19

P(Not black) = 1 - (9/19) = 10/19

Odds against black = P(not black) / P(black) = 10/9

Answer: The odds, in simplified form, should actually be 10 to 9 to make the bet fair

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