# Two balls are chosen randomly from an urn containing 8 white, 4 black, and 2 orange balls

S
40 points

Two balls are chosen randomly from an urn containing 8 white, 4 black, and 2 orange balls. Suppose that we win \$2 for each black ball selected and we lose \$1 for each white ball selected. Let X denote our winnings. What are the possible values of X, and what are the probabilities associated with each value?

probability
random variable

8.7k points

The sample space includes the following scenarios

Balls {W,W} {W,B} {W,O} {B,B} {B,O} {O,O}
X -\$2 \$1 -\$1 \$4 \$2 \$0

probability of -$2 $$P(X=-2)=\frac{C(8,2)}{C(14,2)}=\frac{4}{13}$$ probability of -$1

$$P(X=-1)=\frac{C(8,1)C(2,1)}{C(14,2)}=\frac{16}{91}$$

probability of $0 $$P(X=0)=\frac{C(2,2)}{C(14,2)}=\frac{1}{91}$$ and proceed in this manner for the remaining probabilities, one way to check your answer is they should all sum to 1 ### Your Answer Surround your text in *italics* or **bold**, to write a math equation use, for example, $x^2+2x+1=0\$ or $$\beta^2-1=0$$

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