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 \u25A1 to \u25A1. (Type a whole number.)

Solution

To compute the odds against obtaining a number less than 5 in a single roll of a die, we first find the probability of rolling a number less than 5. A standard die has 6 faces with numbers 1 through 6. The numbers less than 5 are 1, 2, 3, and 4. So, there are 4 favorable outcomes. The total possible outcomes are 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 \[ 1 - \frac{2}{3} = \frac{1}{3} \] Odds against rolling a number less than 5 are calculated as the ratio of the probability of not rolling to rolling a number less than 5: \[ \frac{\frac{1}{3}}{\frac{2}{3}} = \frac{1}{2} \] Therefore, the odds against obtaining a number less than 5 are 1 to 2.