Question

Determine whether the following individual events are independent or dependent. Then find the probability of the combined event.The next 9 births at a hospital all being boys.Choose the correct answer below.(Simplify your answer.)A. The individual events are independent. The probability of the combined event is ___B. The individual events are dependent. The probability of the combined event is ___

Answer 1

Option A

Explanation:

Two events are said to be independent if the outcome of one of the events does not affect the outcome of the other event.

The births in a hospital are independent of one another, thus, the event is independent.

The probability of the birth of a boy = 1/2

Thus, the probability of the next 9 births at a hospital all being boys is:

`\begin{gathered} P(9\text{ births being boys\rparen}=((1)/(2))^9 \\ =(1)/(2^9) \\ =(1)/(512) \end{gathered}`

Therefore, the individual events are independent. The probability of the combined event is 1/512.

Option A is correct.