We choose 2 balls at random from an urn containing 8 white, 4 black and 2 orange. Suppose we receive $2 for each black ball drawn and we lose $1 for each white ball drawn. Let the variable X be “net gains”. Find the probability distribution of X.

We choose 2 balls at random from an urn containing 8 white, 4 black and 2 orange. Suppose we receive $2 for each black ball drawn and we lose $1 for each white ball drawn. Let the variable X be “net gains”. Find the probability distribution of X.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

We choose 2 balls at random from an urn containing 8
white, 4 black and 2 orange. Suppose we receive $2
for each black ball drawn and we lose $1 for each
white ball drawn. Let the variable X be “net gains”. Find the
probability distribution of X.

Expert Solution

Step 1: Determine the given variable

Given:

Total balls = 8 white + 4 black + 2 orange = 14 balls.
Gains for black ball = $2.
Loss for white ball = $1.

Let's enumerate all possible outcomes when drawing 2 balls:

2 white balls: Loss $2. (Net gain X = -$2)
1 white ball and 1 black ball: Gain $2 and loss $1. (Net gain X = $1)
2 black balls: Gain $4. (Net gain X = $4)
1 white ball and 1 orange ball: Loss $1. (Net gain X = -$1)
1 black ball and 1 orange ball: Gain $2. (Net gain X = $2)
2 orange balls: No gain or loss. (Net gain X = $0)

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