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January 29th, 2017, 07:42 AM   #1
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Homework question

Two balls are randomly chosen, without replacement, from an urn containing 8 blue, 4 yellow and
2 green balls. Suppose that we win £2 for each yellow ball selected and lose £1 for each blue ball
selected. Let R be the random variable giving our profit. Find the induced sample space for R and
evaluate the probabilities on the induced sample space.

Hi guys please could you give me maybe a few pointers or hints on how to approach this question, I'm trying to work out the sample space first by using the
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January 29th, 2017, 08:34 AM   #2
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As all colors have at least 2 balls the possible selections can be

$\{BB, YY, GG, BY, BG, YG\}$

The probability, for example, of $BB$ is $\dfrac{8}{14}\dfrac{7}{13} = \dfrac{4}{13}$

Similarly $P[YG] = \dfrac{4}{14}\dfrac{2}{13} = \dfrac{4}{91}$

I leave it to you to find the rest of these probabilities.

Now as $R$ is the profit we get from the described scheme we can map each of these ball selection events into a profit event.

It should be straightforward to see that the above set of pairs of ball colors maps to

$R=\{-2, 4, 0, 1, -1, 2\}$

with $P[-2] = \dfrac {4}{13},~P[2]=\dfrac{4}{91}$, etc.

So the set $R$ above is the induced sample space, and you'll finish finding each of their probabilities.
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January 30th, 2017, 02:33 AM   #3
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In this scenario, one has a good chance of ending up with at least one blue ball and thus coming out ahead in terms of winning money.
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January 30th, 2017, 11:19 AM   #4
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Quote:
Originally Posted by toddhicks209 View Post
In this scenario, one has a good chance of ending up with at least one blue ball and thus coming out ahead in terms of winning money.
Have you even read the problem carefully?

If you pick a blue ball, you lose money.

Maybe you should change your slogan to "Todd gives math tips but does not guarantee that they are correct."
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