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?

Question

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

Answer 1

Hello, thank you for taking the time to post your question!

The give or take for a series of bets is found by multiplying the standard deviation of a single bet by the square root of the number of bets. On this one, we have the standard deviation for a single roulette bet being $5.76 and the number of bets = 1600, meaning you want to take

5.76 * sqrt(1600)

=5.76 * 40

=230.504

So the rounded value here should be the $230.50 for this one

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

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.