MATHEMATICS COLLEGE

An urn contains 11 balls, 3 white, 3 red, and 5 blue balls. Take out two balls at random, without replacement. You win $1 for each red ball you select and lose a $1 for each white ball you select. Let X be the random variable that notes the amount you win. Find the probability mass function (p.m.f.) of X.

Answers

Answer 1

Answer:

Answer with explanation:

Given: An urn contains 11 balls, 3 white, 3 red, and 5 blue balls.

You win $1 for each red ball you select and lose a $1 for each white ball you select.

Let X be the number of times you win.

The total number of ways to select 2 balls (order does not matter) =

The number of ways so that two balls are white (and $X=-2):^3C_2=3$

$P(X=-2)=(3)/(55)$

The number of ways so that two balls are red (and $X=2):^3C_2=3$

$P(X=2)=(3)/(55)$

The number of ways so that one ball is red, one is white (and $X=0):^3C_1*^3C_1=9$

The number of ways so that two balls are blue (and $X=0$ ): $^5C_2=(5 \cdot 4) / 2=10$

i.e. $P(X=0)=(10+9)/(55)=(19)/(55)$

The number of ways so that one ball is blue, one is white (and $X=-1$ ): $^5C_1*^3C_1=15$

$P(X=-1)=(15)/(55) =(3)/(11)$

The number of ways so that one ball is blue, one is red (and $X=1$ ): $^5C_1*^3C_1=15$

$P(X=1)=(15)/(55) =(3)/(11)$

Thus, the probability mass function (p.m.f.) of X would be ( in attachment) :

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Step-by-step explanation:

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Answers

Answer:

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Answers

Answer:

x = −69

Step-by-step explanation:

1: Simplify

−2x−(10)(12)=18

−2x+−120=18

−2x−120=18

2: Add 120 to both sides.

−2x−120+120=18+120

−2x = 138

3: Divide both sides by -2.

-2x ÷ -2 = 138 ÷ -2

x = −69

Answer:

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Answers

Answer:

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Answer:

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Step-by-step explanation:

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