Suzy grabs four marbles from a bag containing three white marbles and six blue marbles. Find the probability that two of the marbles are white, and two are blue.

A) $\frac { 1 } { 6 }$
B) $\frac { 1 } { 14 }$
C) $\frac { 11 } { 42 }$
D) $\frac { 5 } { 14 }$
E) 1

Question

Suzy grabs four marbles from a bag containing three white marbles and six blue marbles. Find the probability that two of the marbles are white, and two are blue.
 
A)  $\frac { 1 } { 6 }$
B)   $\frac { 1 } { 14 }$
C)   $\frac { 11 } { 42 }$
D)   $\frac { 5 } { 14 }$
E)  1

Quizplus · Accepted Answer

The probability of drawing two white marbles and two blue marbles can be calculated using combinations. The number of ways to choose two white marbles out of three is $C(3,2) = 3$, and the number of ways to choose two blue marbles out of six is $C(6,2) = 15$. The total number of ways to choose four marbles out of nine is $C(9,4) = 126$. Therefore, the probability is $\frac{3 \times 15}{126} = \frac{45}{126} = \frac{5}{14}$.

Suzy Grabs Four Marbles from a Bag Containing Three White 16\frac { 1 } { 6 }61​

Suzy Grabs Four Marbles from a Bag Containing Three White $\frac { 1 } { 6 }$