Question: Compute the odds against obtaining a number less than 5 in a single roll of a die. The odds…

Compute the odds against obtaining a number less than 5 in a single roll of a die.

The odds against are \boxed{} to \boxed{}. (Type a whole number.)

Solution

To find the odds against obtaining a number less than 5 in a single roll of a die, we first need to calculate the probability of rolling a number less than 5. A standard die has 6 faces numbered from 1 to 6. The numbers less than 5 on the die are 1, 2, 3, and 4. Therefore, there are 4 favorable outcomes. The total number of possible outcomes is 6. The probability of rolling a number less than 5 is \[ \frac{4}{6} = \frac{2}{3} \] The probability of not rolling a number less than 5 is \[ 1 - \frac{2}{3} = \frac{1}{3} \] The odds against rolling a number less than 5 are given by the ratio of the probability of not rolling a number less than 5 to the probability of rolling a number less than 5: \[ \frac{\frac{1}{3}}{\frac{2}{3}} = \frac{1}{3} \times \frac{3}{2} = \frac{1}{2} \] Thus, the odds against obtaining a number less than 5 are 1 to 2.