Find the probability for the experiment of drawing two marbles (without replacement)from a bag containing two green,five yellow,and three red marbles such that the marbles are different colors.
A) $\frac { 31 } { 90 }$
B) $\frac { 31 } { 15 }$
C) $\frac { 31 } { 45 }$
D) $\frac { 1 } { 5 }$
E) $\frac { 62 } { 9 }$

Question

​Find the probability for the experiment of drawing two marbles (without replacement)from a bag containing two green,five yellow,and three red marbles such that the marbles are different colors.
A)​ $\frac { 31 } { 90 }$
B)​ $\frac { 31 } { 15 }$
C)​ $\frac { 31 } { 45 }$
D)​ $\frac { 1 } { 5 }$
E)​ $\frac { 62 } { 9 }$

Quizplus · Accepted Answer

There are 10 marbles in total, and we need to choose 2 of them. The total number of possible outcomes is:
10 choose 2 = 10!/(2!8!) = 45
To get the marbles of different colors, we can choose one green marble, one yellow marble or one green marble, one red marble, or one yellow marble, one red marble. The number of outcomes with these combinations is: 
2 choose 1 * 5 choose 1 + 2 choose 1 * 3 choose 1 = 10
Therefore, the probability of drawing two marbles of different colors is: 
10/45 = 2/9

​Find the Probability for the Experiment of Drawing Two Marbles 3190\frac { 31 } { 90 }9031​

Find the Probability for the Experiment of Drawing Two Marbles $\frac { 31 } { 90 }$