Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6} , and all the outcomes are equally likely. Find P(less than 2.) Write your answer as a fraction or whole number.

Answer 1

To find the probability of rolling a number less than 2 on a fair die, we first identify the outcomes in the sample space, which is {1, 2, 3, 4, 5, 6}.

The numbers less than 2 in this sample space are:

• 1

There is only 1 outcome (rolling a 1) that is less than 2.

The total number of outcomes when rolling a die is 6.

The probability \( P \) of rolling a number less than 2 is given by the formula:

\[ P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

In this case:

\[ P(\text{less than 2}) = \frac{1}{6} \]

So, the probability of rolling a number less than 2 is \(\frac{1}{6}\).