Question

an american roulette wheel has 38 pockets. in number ranges from 1 to 10 and 19 to 28, odd numbers are red and even are black. in ranges from 11 to 18 and 29 to 36, odd numbers are black and even are red. there are two green pockets numbered 0 and 00. these are neither odd nor even. when playing roulette, a player may choose to place a bet on a single number, various groupings of numbers, the color red or black, whether the number is odd or even, or if the number is high or low. the croupier then spins a wheel in one direction and a ball in the opposite direction. the ball eventually loses momentum and falls into one of the pockets on the wheel. if the ball falls in a pocket that matches your bet, you are a winner. what are the odds for the ball landing in an even - numbered slot? what are the odds against the ball landing in an even - numbered slot? provide your answers in lowest terms (reduce).

Explanation:

Step1: Determine total non - green pockets

There are 38 pockets in total with 2 green pockets (0 and 00). So the number of non - green pockets is $38 - 2=36$.

Step2: Determine number of even non - green pockets

Out of 36 non - green pockets, half are even. So the number of even non - green pockets is $\frac{36}{2}=18$.

Step3: Determine number of odd non - green pockets

The number of odd non - green pockets is also 18 (since non - green pockets are evenly split between odd and even).

Step4: Calculate odds for landing in an even - numbered slot

The odds for an event is the ratio of the number of favorable outcomes to the number of non - favorable outcomes. For landing in an even - numbered slot, the number of favorable outcomes (even non - green pockets) is 18 and non - favorable outcomes (odd non - green pockets + green pockets) is $18 + 2=20$. So the odds for are $18:20 = 9:10$.

Step5: Calculate odds against landing in an even - numbered slot

The odds against an event is the ratio of the number of non - favorable outcomes to the number of favorable outcomes. So the odds against are $20:18=10:9$.

Answer:

For odds for: 9 to 10
For odds against: 10 to 9