Question

A ping pong ball is drawn at random from an urn consisting of balls numbered 4 through 9. A player wins $1.5 if the number on the ball is odd and loses $0.5 if the number is even.

Let x be the amount of money a player will win/lose when playing this game, where x is negative when the player loses money.

(a) Construct the probability table for this game. Round your answers to two decimal places.

Outocme	x	Probability P(x)

(b) What is the expected value of player's winnings? Round to the nearest hundreth.



(c) Interpret the meaning of the expected value in the context of this problem.

Answer 1

There are 6 balls numbered 4 through 9. Each is equally likely to be drawn . Thus , each will have Probability of 1/6.

If number on the drawn urn is even then , the player loses $0.5 ( X = -0.5) and if number is odd , then the player wins $1.5 ( x = 1.5)

	X	Probability
Ball numbered 4 (even)	-0.5	1/6
Ball numbered 5 (odd)	1.5	1/6
Ball numbered 6 (even)	-0.5	1/6
Ball numbered 7 (odd)	1.5	1/6
Ball numbered 8 (even)	-0.5	1/6
Ball numbered 9 (odd)	1.5	1/6

a) Thus , the Probability Distribution is :

X p(x)

1.5 0.5

-0.5 0.5

b) Expected Value is given by :

E(x) = x* p(x)

X	P(x)	x * P(x)
1.5	0.5	0.75
-0.5	0.5	-0.25

E(x) = 0.75 - 0.25

E(x) = 0.5

Thus , the expected value of players winnings is $ 0.5.

c) Interpretation: In the long run , over an average a player win $0.5 with this game.

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