Question

Consider a dice being thrown. Find the following probability.

P(rolling a 3 OR an even number)

Question 1 options:

0.25


0.84


0.67


0.33

Answer 1

To find the probability of rolling a 3 or an even number on a standard six-sided die, we first identify the relevant outcomes.

The possible outcomes when throwing a die are:
1, 2, 3, 4, 5, 6.

Now, we determine the favorable outcomes for the event "rolling a 3 or an even number."

1. The event of rolling a 3 has 1 favorable outcome: {3}.
2. The event of rolling an even number includes: {2, 4, 6} which has 3 favorable outcomes.

Now, let's combine these events. The event of rolling a 3 and rolling an even number is mutually exclusive. Therefore, we can simply add the number of favorable outcomes:

- Favorable outcomes for rolling a 3: 1
- Favorable outcomes for rolling an even number: 3
- Total favorable outcomes: 1 + 3 = 4

Now, the total number of possible outcomes when rolling a die is 6.

Thus, the probability \( P \) of rolling a 3 or an even number is given by the formula:

\[
P(\text{rolling a 3 or an even number}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{4}{6} = \frac{2}{3} \approx 0.67
\]

So, the answer is:

**0.67**