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


S
Asked by 4 years ago
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

1 Answer

Answered by 4 years ago
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

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Views: 55
Asked: 4 years ago

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