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*.

**Please like the answer,Thanks!**

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ball is odd and loses $1.5 if the number is even.
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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
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