Let's go through each question in turn and calculate the probabilities as requested.

1. Probability that the sum of two dice is 11

When rolling two six-sided dice, each die has 6 possible outcomes (1 through 6). The total number of possible outcomes is $6 \times 6 = 36$. We need to find outcomes where the sum of the dice equals 11.

The pairs that sum to 11 are:

• (5,6)
• (6,5)

There are 2 outcomes where the sum is 11. Therefore, the probability of getting a sum of 11 is: $\frac{2}{36} = \frac{1}{18}$

2. Probability of selecting a red shirt from a bag

The bag contains:

• 4 red shirts
• 6 blue shirts
• 8 black shirts

The total number of shirts is: $4 + 6 + 8 = 18$

The probability of selecting a red shirt is the ratio of red shirts to the total number of shirts: $\frac{4}{18} = \frac{2}{9}$

3. Probability of a customer buying a Sony camera or buying from Walmart

Let's calculate the probability of either buying a Sony camera or buying from Walmart using the provided table.

Total customers who bought a Sony camera:

• Sony at Best Buy: 33
• Sony at Walmart: 48 $33 + 48 = 81$

Total customers who bought a camera at Walmart:

• Walmart total: 177

Customers who bought a Sony camera at Walmart (to avoid double-counting):

$48$

Using the formula for the probability of $A$ or $B$: $P(\text{Sony or Walmart}) = P(\text{Sony}) + P(\text{Walmart}) - P(\text{Sony and Walmart})$ $= \frac{81}{300} + \frac{177}{300} - \frac{48}{300} = \frac{210}{300} = \frac{7}{10}$

So, the probability that a randomly selected customer bought a Sony camera or purchased from Walmart is $\frac{7}{10}$.

4. Union of Events A and B

The union of Events A and B, denoted $A \cup B$, represents the occurrence of either Event A or Event B or both. If we let $n(A)$ and $n(B)$ represent the number of instances in which Event A and Event B occur, respectively, and $n(A \cap B)$ represent the number of instances where both occur, then: $n(A \cup B) = n(A) + n(B) - n(A \cap B)$

This formula ensures we don’t double-count instances where both events occur.

Let me know if you would like further explanation or have questions about any part.

Further Questions:

1. How would you find the probability of getting a sum of 7 when rolling two dice?
2. What is the probability of selecting a blue shirt from the bag in Question 2?
3. How would the probability change in Question 3 if the total customers were different?
4. How do we calculate the probability of both events $A$ and $B$ occurring simultaneously?
5. What is the difference between the union and intersection of two events?

Tip: When calculating probabilities with overlapping events, always remember to subtract the probability of their intersection to avoid double-counting.