Let's go through each of the questions in the image.

Question 28:

We are given:

• $P(A) = 0.8$
• $P(B) = 0.2$
• $P(A \cap B) = 0.16$

We need to determine the relationship between events $A$ and $B$.

1. Check if $A$ and $B$ are independent: Two events $A$ and $B$ are independent if: $P(A \cap B) = P(A) \times P(B)$ Let's check: $P(A) \times P(B) = 0.8 \times 0.2 = 0.16$ Since $P(A \cap B) = 0.16$, $A$ and $B$ are independent.

2. Check if $A$ and $B$ are disjoint: Two events are disjoint if $P(A \cap B) = 0$. Since $P(A \cap B) = 0.16 \neq 0$, the events are not disjoint.

So, the correct answer is:

• B) Independent but not disjoint.

Question 29:

We are asked to identify the sample points in the event $A \cap B$.

• $A$ is the event where the number is even: $A = \{2, 4, 6, 8, 10\}$.
• $B$ is the event where the number is less than 7: $B = \{1, 2, 3, 4, 5, 6\}$.

The event $A \cap B$ represents the numbers that are in both $A$ and $B$. So, we need to find the intersection of the two sets: $A \cap B = \{2, 4, 6\}$

Therefore, the correct answer is:

• C) {2, 4, 6}.

Would you like further details or explanations on any part of these solutions? Here are 5 related questions that you could explore:

1. How do you test if two events are disjoint using probabilities?
2. What is the difference between disjoint and independent events?
3. How do you calculate the intersection of two events with known probabilities?
4. If $P(A) = 0.8$, what is the probability of the complement of event $A$?
5. How does the concept of mutually exclusive events apply to real-life situations?

Tip: Always double-check whether two events are independent by comparing $P(A \cap B)$ to $P(A) \times P(B)$.