Alright, let's solve this problem step-by-step.
Given: Glenn rolls a 6-sided die, which has possible outcomes of 1, 2, 3, 4, 5, and 6.
We are asked to find the probability of rolling a number greater than 2 or an odd number.
### Step 1: Identify Numbers Greater Than 2
The numbers greater than 2 on the die are 3, 4, 5, and 6. Thus, we have:
[tex]\[ \{ 3, 4, 5, 6 \} \][/tex]
### Step 2: Identify Odd Numbers
The odd numbers on the die are 1, 3, and 5. Thus, we have:
[tex]\[ \{ 1, 3, 5 \} \][/tex]
### Step 3: Find the Union of the Two Sets
We need to combine the sets of numbers greater than 2 and the odd numbers to find the favorable outcomes. The union of the two sets is:
[tex]\[ \{ 1, 3, 4, 5, 6 \} \][/tex]
### Step 4: Count the Number of Favorable Outcomes
Count the elements in the union set:
[tex]\[ \{ 1, 3, 4, 5, 6 \} \][/tex]
There are 5 numbers in this set.
### Step 5: Calculate the Total Possible Outcomes
Since the die is 6-sided, there are 6 possible outcomes in total.
### Step 6: Determine the Probability
The probability of the favorable outcomes is the number of favorable outcomes divided by the total number of possible outcomes:
[tex]\[ P(\text{favorable}) = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}} = \frac{5}{6} \][/tex]
### Step 7: Choose the Closest Option
We compare \(\frac{5}{6}\) with the provided options:
- \(\frac{2}{3}\)
- \(\frac{5}{6}\)
- \(\frac{3}{4}\)
- \(\frac{1}{3}\)
Clearly, \(\frac{5}{6}\) matches perfectly with one of the options.
Thus, the correct answer is:
[tex]\[ \boxed{\frac{5}{6}} \][/tex]
