To determine the probabilities for each of the scenarios when rolling a six-sided die, we will first identify the possible outcomes. A standard six-sided die has six faces, numbered from 1 to 6.
Case A: Rolling a 5 or a Number Greater Than 3
The numbers that are 5 or greater than 3 on the die are: 4, 5, and 6. Therefore, the successful outcomes for this scenario are:
- 4
- 5
- 6
This gives us a total of 3 successful outcomes. The total number of possible outcomes when rolling the die is 6. Thus, the probability can be calculated using the formula:
Probability = (Number of Successful Outcomes) / (Total Number of Possible Outcomes)
Substituting the values, we get:
Probability = 3 / 6 = 1 / 2
This means there is a 50% chance of rolling a 5 or a number greater than 3.
Case B: Rolling a Number Less Than 5
The numbers that are less than 5 on a six-sided die are: 1, 2, 3, and 4. Therefore, the successful outcomes for this scenario are:
- 1
- 2
- 3
- 4
This gives us a total of 4 successful outcomes. Using the same total of 6 possible outcomes, we calculate the probability for this scenario:
Probability = (Number of Successful Outcomes) / (Total Number of Possible Outcomes)
Substituting the values, we get:
Probability = 4 / 6 = 2 / 3
Thus, there is a 66.67% chance of rolling a number less than 5.