A bag contains 2 gold marbles, 9 silver marbles, and 20 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1.

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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A bag contains 2 gold marbles, 9 silver marbles, and 20
black marbles. Someone offers to play this game: You
randomly select one marble from the bag. If it is gold, you
win $3. If it is silver, you win $2. If it is black, you lose $1.
What is your expected value if you play this game?
Transcribed Image Text:A bag contains 2 gold marbles, 9 silver marbles, and 20 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1. What is your expected value if you play this game?
Expert Solution
Step 1

Given information:

There are 2 gold marbles, 9 silver marbles and 20 black marbles.

Total number of marbles is, 2+9+20=31.

Here,

P(gold marble)=2/31

P(silver marble)=9/31

P(black marble)=20/31

If the marble is gold, then you win $3.

That is, x=3 and P(x=3)=2/31.

If the marble is silver, then you win $2.

That is, x=2 and P(x=2)=9/31.

If the marble is black, then you lose $1.

That is, x=-1 and P(x=-1)=20/31.

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