A gambler bets 1 on the number 19 1600 times in roulette Thi

A gambler bets $1 on the number \"19\" 1600 times in roulette. This bet pays 35 to 1. What is the give-or-take on the estimate of his winnings?

a. $184.25
b. $96.58
c. $230.50
d. $84.36
e. $23.50

Solution

Assuming that it is American roulette, The number 19 appears once out of 38 other numbers. that means you have a 1/38 probability of winning.

that 1/38 chance will pay you $35 and the 37 other ties will pay you $-1. So let\'s say you play only 38 times. Probability says you will lose 37 times and win once, meaning you will lose $37 and win $35. All in all you lose $2 every 38 tries. How many groups of 38 tries is there in 1600? 42.105. Multiply that by -2 and you get 84.21, which is close enough to 84.36 with the error being a difference of rounding.