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

Answered by Aaron 4 years ago

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

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Asked: 4 years ago