Question

Suppose you roll a standard number cube. What is the probability of rolling a number less than 3 or an odd number?(1 point)
Responses

1
3
Start Fraction 1 over 3 End Fraction

5
6
Start Fraction 5 over 6 End Fraction

2
3
Start Fraction 2 over 3 End Fraction

1
2

Answer 1

To solve the problem, we first identify the numbers on a standard cube (number cube) which are 1, 2, 3, 4, 5, and 6.

**Step 1: Find the numbers that are less than 3.**
- The numbers less than 3 are: 1, 2.
- So there are 2 favorable outcomes.

**Step 2: Find the odd numbers on the cube.**
- The odd numbers on the cube are: 1, 3, 5.
- So there are 3 favorable outcomes.

**Step 3: Combine the two sets of outcomes.**
- We are looking for the probability of either rolling a number less than 3 or an odd number.

Let’s list out the outcomes:
- Numbers less than 3: {1, 2}
- Odd numbers: {1, 3, 5}

Now, combine these outcomes:
- Combined outcomes: {1, 2, 3, 5}

Notice that rolling a 1 is counted in both sets, but we only count it once.

**Total unique outcomes** = {1, 2, 3, 5} = 4 favorable outcomes.

**Step 4: Calculate the total number of outcomes when rolling a die.**
- There are a total of 6 outcomes (1 through 6).

**Step 5: Calculate the probability.**
The probability of rolling a number less than 3 or an odd number is:
\[ P(A \cup B) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{4}{6} = \frac{2}{3}. \]

So the correct response is:
**Start Fraction 2 over 3 End Fraction**.