What is the probability of rolling a 5 or a number greater than 3 on a six-sided die, and what is the probability of rolling a number less than 5?

by

Calculating Probabilities with a Six-Sided Die

A standard six-sided die has six faces, numbered from 1 to 6. To find probabilities for specific scenarios, we can use the formula:

Probability (P) = Number of favorable outcomes / Total number of possible outcomes

Scenario A: Rolling a 5 or a Number Greater than 3

First, let’s identify the outcomes that meet this condition:

  • Rolling a 5
  • Rolling a 4
  • Rolling a 6

Thus, the favorable outcomes for this scenario are 4, 5, and 6. That gives us a total of three favorable outcomes.

The total possible outcomes when rolling a six-sided die are 6 (which are 1, 2, 3, 4, 5, 6). Therefore, the probability of rolling a 5 or a number greater than 3 is:

P(5 or >3) = 3 favorable outcomes / 6 total outcomes = 1/2 or 0.5

Scenario B: Rolling a Number Less than 5

Now, let’s consider the second scenario where we want to find the probability of rolling a number less than 5. The numbers that are less than 5 on the die are:

  • 1
  • 2
  • 3

The favorable outcomes in this case are 1, 2, and 3, making a total of three favorable outcomes as well.

Using the same total possible outcomes of 6, we can calculate the probability:

P(<5) = 3 favorable outcomes / 6 total outcomes = 1/2 or 0.5

Summary

In conclusion, the probabilities for the scenarios are as follows:

  • Probability of rolling a 5 or a number greater than 3: 0.5
  • Probability of rolling a number less than 5: 0.5

Leave a Comment