A bag contains 30 white marbles and 30 black marbles. If 8 marbles are chosen, what is the probability that there will be 2 white marbles and 6 black marbles?
A)$\frac { { } _ { 6 } ^ { C _ { 2 } } { } _ { 30 } C _ { 30 } } { 60 }$

B) $60 C _ { 8 }$

C) $\frac { 3 { } ^ { 3 } C _ { 2 } { } _ { 30 } C _ { 6 } } { { } _ { 60 } C _ { 8 } }$

D) $\frac { 60 ^ { C _ { 8 } } } { { } _ { 30 } C _ { 23 } { } _ { 30 } C }$

Question

A bag contains 30 white marbles and 30 black marbles. If 8 marbles are chosen, what is the probability that there will be 2 white marbles and 6 black marbles? 
A)$\frac { { } _ { 6 } ^ { C _ { 2 } } { } _ { 30 } C _ { 30 } } { 60 }$

B) $60 C _ { 8 }$

C) $\frac { 3 { } ^ { 3 } C _ { 2 } { } _ { 30 } C _ { 6 } } { { } _ { 60 } C _ { 8 } }$

D) $\frac { 60 ^ { C _ { 8 } } } { { } _ { 30 } C _ { 23 } { } _ { 30 } C }$

Quizplus · Accepted Answer

The correct probability is calculated by choosing 2 white marbles out of 30 and 6 black marbles out of 30, divided by the total ways to choose 8 marbles out of 60. This is represented by $\frac{{}_{30}C_{2} \times {}_{30}C_{6}}{{}_{60}C_{8}}$.

A Bag Contains 30 White Marbles and 30 Black Marbles 6C230C3060\frac { { } _ { 6 } ^ { C _ { 2 } } { } _ { 30 } C _ { 30 } } { 60 }606C2​​30​C30​​

A Bag Contains 30 White Marbles and 30 Black Marbles $\frac { { } _ { 6 } ^ { C _ { 2 } } { } _ { 30 } C _ { 30 } } { 60 }$