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Determine whether the following individual events are independent or dependent. Then find the probability of the combined event. Randomly selecting a four-person committee consisting entirely of from a pool of 9 Americans and 14 Canadians.Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.(Type an integer or a simplified fraction.)A.The individual events are overlapping. The probability of the combined event is   enter your response here.B.The individual events are non-overlapping. The probability of the combined event is   enter your response here.

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Given

The event as,

Randomly selecting a​ four-person committee consisting entirely of from a pool of 9 Americans and 14 Canadians.

To determine whether the individual events are independent or dependent.

Also, to find the probability of the combined event.

Step-by-step explanation:

The given individual events are independent.

Then, the probability of the combined event is,


\begin{gathered} P(AB)=P(A)\cdot P(B) \\ =9C_4*14C_4 \\ =(9!)/((9-4)!4!)*(14!)/((14-4)!4!) \\ =\frac{9*8*7\operatorname{*}6\operatorname{*}5!}{5!(4\operatorname{*}3\operatorname{*}2\operatorname{*}1)}*\frac{14*13*12\operatorname{*}11\operatorname{*}10!}{10!(4\operatorname{*}3\operatorname{*}2\operatorname{*}1)} \\ =\frac{9*8*7\operatorname{*}6}{8*3}*\frac{14*13*12\operatorname{*}11}{12*2} \\ =3*42*7*11*13 \\ =126*77*13 \\ =126126 \end{gathered}

Hence, the probability of the combined event is 126126.

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