The image you provided shows a probability problem where you are calculating the probability of sums from rolling two dice.

1. Part 1 (a) asks for the probability of getting a sum of 2 when two dice are rolled. The probability given is $P(\text{sum of 2}) = 0.028$.

2. Part 2 (b) asks for the probability of getting a sum of 6 or a sum of 3. You need to calculate $P(\text{sum of 6 or 3})$.

Solution Steps:

For (b) A sum of 6 or 3:

When rolling two dice, there are a total of $6 \times 6 = 36$ possible outcomes (since each die has 6 faces).

• Sum of 6: The outcomes that result in a sum of 6 are:

  • (1, 5), (2, 4), (3, 3), (4, 2), (5, 1) — Total: 5 outcomes.

• Sum of 3: The outcomes that result in a sum of 3 are:

  • (1, 2), (2, 1) — Total: 2 outcomes.

Thus, the total number of favorable outcomes is $5 + 2 = 7$.

Probability:

The probability of getting a sum of 6 or 3 is the number of favorable outcomes divided by the total number of possible outcomes: $P(\text{sum of 6 or 3}) = \frac{7}{36} \approx 0.194$

Would you like more details on this calculation or on the concepts of probability?

Here are 5 follow-up questions to expand on this topic:

1. How do you calculate the probability of mutually exclusive events like rolling a sum of 6 or 3?
2. What would the probability be if you wanted a sum of 5 or 7?
3. How does the total number of possible outcomes change if we add more dice?
4. How does the probability change if only one die is rolled, and you need specific outcomes?
5. How can you apply this concept of probabilities to card games or other random experiments?

Tip:

When calculating probabilities involving multiple outcomes, remember to check if the events are mutually exclusive or independent, as it affects how you sum the probabilities.