The question involves calculating the probability for three scenarios when rolling a six-sided die. Let's go through each part.

Part (c)

Let's solve for:

(c) Rolling a 2 or an odd number.

Solution

1. Possible outcomes on a six-sided die: {1, 2, 3, 4, 5, 6}.

2. Event: Rolling a 2 or an odd number:

   • Odd numbers on a die: {1, 3, 5}.
   • Including the 2, the favorable outcomes are: {1, 2, 3, 5}.

3. Counting favorable outcomes:

   • There are 4 favorable outcomes: {1, 2, 3, 5}.

4. Total possible outcomes:

   • Since there are six faces on the die, there are 6 possible outcomes in total.

5. Calculating the probability: $P(\text{Rolling a 2 or an odd number}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{4}{6} = 0.667$

Answer

So, the probability for part (c) is: $P(2 \text{ or an odd number}) = 0.667$ (rounding to three decimal places as requested).

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Additional Related Questions

1. What is the probability of rolling a number greater than 4 on a six-sided die?
2. If rolling two six-sided dice, what is the probability that the sum is an odd number?
3. What is the probability of rolling a prime number on a six-sided die?
4. How would the probability change if using an eight-sided die for these calculations?
5. What is the probability of rolling an even number on a standard six-sided die?

Tip

When dealing with probabilities, always identify the favorable outcomes first, and then divide by the total possible outcomes to calculate the probability.