Question 1020068
In American roulette, there are 38 bins, 18 red, 18 black, 0 and 00 (both green).
A red bet has the probability of 
{{{P(R)=18/38=9/19}}}
a) The probability of each spin is independent of previous results.
{{{P(R)=9/19}}}
b){{{P(RRR)=(9/19)^3=729/6859}}}
c) The payout on winning is 1:1 on red. So you win $1 if you bet $1. Let's look at her expected winnings for one hand and multiply it by 3.
{{{E=(9/19)*1-(10/19)1=-1/19}}}
So she should expect to lose 5.3 cents each time, in 3 hands 15.7 cents.
d) As you see from c), although people can and do win big occasionally on average and over time, the casino will win, slowly but surely. Otherwise they wouldn't be in business. You can fill in with additional words.