What is the probability of rolling an odd number or a number less than 3 when a fair die is rolled?

by

To determine the probability of rolling an odd number or a number less than 3 on a fair six-sided die (which has the numbers 1 through 6), we need to identify the favorable outcomes for each condition and then combine them.

Step 1: Identify the Total Outcomes

A fair die has 6 sides, so there are a total of 6 possible outcomes when the die is rolled: {1, 2, 3, 4, 5, 6}.

Step 2: Identify Favorable Outcomes

Odd Numbers: The odd numbers on the die are 1, 3, and 5. Therefore, the favorable outcomes for rolling an odd number are:

  • 1
  • 3
  • 5

This gives us a total of 3 favorable outcomes for rolling an odd number.

Numbers Less than 3: The numbers less than 3 on the die are 1 and 2. Therefore, the favorable outcomes for rolling a number less than 3 are:

  • 1
  • 2

This gives us a total of 2 favorable outcomes for rolling a number less than 3.

Step 3: Combine the Outcomes

Now, we need to consider which outcomes are counted in both categories. The number 1 is an odd number and also less than 3, so it’s essential to avoid double-counting this outcome. Here are the distinct favorable outcomes:

  • 1 (odd and less than 3)
  • 2 (less than 3)
  • 3 (odd)
  • 5 (odd)

This results in a total of 4 distinct favorable outcomes: {1, 2, 3, 5}.

Step 4: Calculate the Probability

The probability of an event is calculated as:

P(Event) = (Number of Favorable Outcomes) / (Total Outcomes)

Using the figures from above:

P(Odd number or number less than 3) = 4 / 6

This simplifies to:

P = 2 / 3

Conclusion

Thus, the probability of rolling an odd number or a number less than 3 when rolling a fair die is 2/3 or approximately 66.67%.

Leave a Comment