Question

You go to the casino and play roulette. You decide to place bets that the ball will land on the number 18. On a roulette wheel there are the numbers 1-36 and 00. Thus, the likelihood that you win any one spin is 1 in 38. You decide to play 20 times, thus you are in binomial land and the potential ersults of your gambling will be drawn from a binomial distribution B(20,1/38). What is the probability that you win:

1) 1 time?

2) 3 times?

Instead of placing bets on a single number, you decide to place bets that the ball will land on a red number. On a roulette wheel there are 18 red and 18 black numbers while the two green are 1 and 00.

3) what is the probability of success for any single spin?

4) What is the probability that if you play 6 spins, you win exactly 3 of them?

If you have a binomial distribution B(n,p), then the distribution in 'a' will have

5) mean=?

6) sigma=?

Answer 1

Given the random variable the number of plays won out of 20 follows Binomial distribution with
The PMF of is

1) The probability,

2) The probability,

3) The probability of success for any single spin is

4)The probability,

5) The mean is

6) The standard deviation is