Respuesta :
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.
Explanation:
The given individual events are independent.
Then, the probability of the combined event is,
[tex]\begin{gathered} P(AB)=P(A)\cdot P(B) \\ =9C_4\times14C_4 \\ =\frac{9!}{(9-4)!4!}\times\frac{14!}{(14-4)!4!} \\ =\frac{9\times8\times7\operatorname{\times}6\operatorname{\times}5!}{5!(4\operatorname{\times}3\operatorname{\times}2\operatorname{\times}1)}\times\frac{14\times13\times12\operatorname{\times}11\operatorname{\times}10!}{10!(4\operatorname{\times}3\operatorname{\times}2\operatorname{\times}1)} \\ =\frac{9\times8\times7\operatorname{\times}6}{8\times3}\times\frac{14\times13\times12\operatorname{\times}11}{12\times2} \\ =3\times42\times7\times11\times13 \\ =126\times77\times13 \\ =126126 \end{gathered}[/tex]Hence, the probability of the combined event is 126126.
