Final answer:
The births of boys at a hospital are independent events. The probability of the next three births all being boys is 0.125.
Step-by-step explanation:
In order to determine whether the events are independent or dependent, we need to analyze the information given. The question states that the next three births at a hospital are all boys.
The probability of each birth being a boy is independent of the previous births, since the gender of one baby does not affect the gender of another baby.
Therefore, the events are independent.
To find the probability of the combined event, we simply multiply the individual probabilities together, since the events are independent.
If the probability of a single birth being a boy is 0.5, then the probability of the next three births all being boys is:
P(3 boys) = P(1 boy) * P(1 boy) * P(1 boy) = 0.5 * 0.5 * 0.5 = 0.125