Question

2. The probability that Gary and Jane have a child

with blue eyes is 0.25, and the probability that they
have a child with blond hair is 0.5. The probability
that they have a child with both blue eyes and
blond hair is 0.125. Given this information, the
events blue eyes and blond hair are
1: dependent
II: independent
III: mutually exclusive
1 I, only
2 II, only
3 I and III
4. Land III

Answer 1

Answer: 2 II, only

Explanation:

The events are independent

Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring. Comparing with the given situation, it means that the fact that the child has blue eyes does not mean that the child would necessarily have blond hair.

The multiplication rule is applied for independent events. Since events A and B are independent, the probability of both occurring is

P(A and B) = P(A) × P(B)

Applying it to the given situation, the probability of the child having blue eyes and blond hair is

0.25 × 0.5 = 0.125

This corresponds to the given probability. Therefore, they are independent events.

Mutually exclusive is not correct because the events can happen at the same time