You roll a fair six-side die. What is the probability of the die showing an odd number or a number greater than two
Out of your 6 choices on a die, there are 2 that are odd and greater than 2,
so prob(your event) = ...
Good
To find the probability of the die showing an odd number or a number greater than two, we need to count the number of favorable outcomes and divide it by the total number of possible outcomes.
The favorable outcomes are the odd numbers (1, 3, 5) and the numbers greater than two (3, 4, 5, 6).
Therefore, the favorable outcomes are 1, 3, 4, 5, and 6.
The total number of possible outcomes is six because there are six sides on the die.
So, the probability of the die showing an odd number or a number greater than two is 5/6 or approximately 0.8333.
To find the probability of an event, you need to divide the number of favorable outcomes by the total number of possible outcomes.
In this case, let's determine the number of favorable outcomes and the total number of possible outcomes separately.
1. Favorable outcomes:
- Odd numbers: There are three odd numbers on a six-sided die, which are 1, 3, and 5.
- Numbers greater than two: There are four numbers greater than two, which are 3, 4, 5, and 6.
To calculate the total number of favorable outcomes, we need to make sure we don't count the common elements twice. Therefore, we count the unique outcomes, which are 1, 3, 4, 5, and 6. So, there are five favorable outcomes.
2. Total possible outcomes:
A fair six-sided die has six possible outcomes, which are 1, 2, 3, 4, 5, and 6.
Now, we can calculate the probability:
Probability = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes)
Probability = 5 / 6
Therefore, the probability of the die showing an odd number or a number greater than two is 5/6 or approximately 0.8333.