Remember that the spins of the wheel are independent and that Appendix B has the
ID: 3209295 • Letter: R
Question
Remember that the spins of the wheel are independent and that Appendix B has the Probability Reference Sheet with Roulette bet explanations. Suppose you are going to spin a European Roulette wheel twice in a row. Find the following, showing work and 4 decimal places. a) You place a "3^rd Dozen" bet on the first spin and then decide a "30/32 Corner" bet on the second spin. What is the probability that you win on both spins? b) You place a "Straight Up 5" bet for both spins. What is the probability that you win on both spins? c) You decide to bet "3^rd Dozen" for both spins. What is the probability that you lose on both spins? d) You decide to bet "13 Street" for both spins. What is the probability that you win on at least one spins?Explanation / Answer
a.
First spin : Bet on 3rd dozen
No. of options in a roulette = 37 (1:36) and a '0'
No. of favorable options for 3rd dozen = 12 (25 to 36)
Probability of winning in first spin = 12/37
Second spin : Bet on 30/32 corner
No. of favorable options for 30/32 corner = 4(29,30,32,33)
Probability of winning in second spin = 4/37
Probability of winning both the spins = Probability of winning in first spin x Probability of winning in second spin = 12/37 x 4/ 37 = 0.0351
b.
First spin : bet on Straight up '5'
No. of favorable options for Straight up '5' = 1
Probability of winning first spin = 1/37
second spin : bet on Straight up '5'
No. of favorable options for Straight up '5' = 1
Probability of winning second spin = 1/37
Probability of winning both the spins = Probability of winning in first spin x Probability of winning in second spin = 1/37 x 1/37 = 0.00073
c.
First spin : bet on 3rd dozen
No. of favorable options for 3rd dozen = 12 (25 to 36)
Probability of winning in first spin = 12/37
First spin : bet on 3rd dozen
No. of favorable options for 3rd dozen = 12
Probability of winning second spin = 12/37
Probability of winning both the spins = Probability of winning in first spin x Probability of winning in second spin = 12/37 x 12/37 = 0.1052
Spin 1: bet on 13 street
No. of favorable options for 13 street = 3 (13,14,15)
Probability of winning in first spin = 3/37
Spin2 : 13 street
No. of favorable options for 13 street = 3 (13,14,15)
Probability of winning in first spin = 3/37
Probability of winning on atleast one spin =
Probability of winning in first spin + Probability of winning in second spin - Probability of winning in both the spins.
Probability of winning in both the spins =Probability of winning in first spin x Probability of winning in second spin = 3/37 x 3/37 = 9/1369
Probability of winning on atleast one spin =
Probability of winning in first spin + Probability of winning in second spin - Probability of winning in both the spins.
= 3/37 + 3/37 - 9/1369 = 6/37 - 9/1369 = 0.324324 - 0.006574 = 0.31775