When playing American roulette, the croupier (attendant) spins a marble that lands in one of the 38 slots:

1. When playing American roulette, the croupier (attendant) spins a marble that lands in one of the 38 slots in a revolving turntable. The slots are numbered 1 to 36, with two additional slots labeled 0 and 00 that are painted green. Assume a single spin of the roulette wheel is made. Find the probability of winning with the given bet. An example of a dozen bet is betting that the marble will land in a slot numbered 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, or 28.

Answer: The total number of outcomes is equal to the total number of slots. The total number of outcomes is 38. The probability of winning the given dozen bet is obtained by getting the number of events divided by entire the sample space. The probability of winning the given dozen bet is obtained by getting the number of events divided by entire the sample space. That is 12/38. Simplifying gives 6/19.

2. When playing American roulette, the croupier (attendant) spins a marble that lands in one of the 38 slots in a revolving turntable. The slots are numbered 1 to 36, with two additional slots labeled 0 and 00 that are painted green. Consider the numbers 0 and 00 as neither even nor odd. Half the remaining slots are colored red and half are black. Assume a single spin of the roulette wheel is made. Find the probability of the marble landing on a green or black slot.

Answer: Slots are numbered 1 to 36
Two additional labeled 0 and 00
So total slots are 36,0,00 which is 38 slots
Therefore, the total number of outcomes is 38
Number of green slots (0,00) =2
Number of black slots =18
Also, the number of outcomes in the event is (number of green slots added to the number of black slots) =18+2= 20
The probability of the marble landing on a green or black slot is 20/38=10/19

3. When playing American roulette, the croupier (attendant) spins a marble that lands in one of the 38 slots in a revolving turntable. The slots are numbered 1 to 36, with two additional slots labelled 0 and 00 that are painted green. Consider the numbers 0 and 00 as neither even nor odd. Half the remaining slots are colored red and half are black. Assume a single spin of the roulette wheel is made. Find the probability of the marble landing on a 0 or black slot.

Answer: Slots are numbered 1 to 36
Two additional labeled 0 and 00
So total slots are 36,0,00 which is 38 slots
Therefore, the total number of outcomes is 38
P(O) or P(black)=1/38+18/38=1/2
It is ½

4. When playing American roulette, the croupier (attendant) spins a marble that lands in one of the 38 slots in a revolving turntable. The slots are numbered 1 to 36, with two additional slots labelled 0 and 00 that are painted green. Consider the numbers 0 and 00 as neither even nor odd. Half the remaining slots are coloured red and half are black. Assume a single spin of the roulette wheel is made. Find the probability of the marble landing on a 0 or even slot.

Answer:18 slots red
18 slots black
36 slots are either even or odd (Implying half will be even, half is odd)
2 slots green (neither even nor odd)
P(0) or even=1/38+18/38=1/2

5. When playing American roulette, the croupier (attendant) spins a marble that lands in one of the 38 slots in a revolving turntable. The slots are numbered 1 to 36, with two additional slots labelled 0 and 00 that are painted green. Assume a single spin of the roulette wheel is made.  Find the probability of winning with the given bet. An example of a bet is betting that the marble will land in a slot numbered 24,25,26,27,28.

Answer
Since there are five bets in total, the probability of winning a bet is 5/38