Question
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.
Answers
GPT-4o mini
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 \(\frac{1}{6}\).
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 \(\frac{1}{6}\).