Question

an american roulette wheel has 38 slots: two slots are numbered 0 and 00, and the remaining slots are numbered from 1 to 36. what are the odds for the ball landing in an odd - numbered slot? to what are the odds against the ball landing in an odd - numbered slot? to simplify your answers.

Explanation:

Step1: Count odd - numbered slots

The numbers from 1 to 36 have 18 odd - numbered slots. The total number of slots is 38.

Step2: Calculate odds for landing in odd - numbered slot

The odds for an event is the ratio of the number of favorable outcomes to the number of non - favorable outcomes. The number of favorable outcomes (landing in an odd - numbered slot) is 18, and the number of non - favorable outcomes is \(38 - 18=20\). So the odds for are \(18:20 = 9:10\).

Step3: Calculate odds against landing in odd - 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:

The odds for the ball landing in an odd - numbered slot: 9 to 10
The odds against the ball landing in an odd - numbered slot: 10 to 9