Question

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 $1.5 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

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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...

A ping pong ball is drawn at random from an urn consisting of
balls numbered 4 through 9. A player wins $0.5 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...

Suppose that a ball is selected at random from an urn with balls
numbered from 1 to 100, and without replacing that ball in the urn,
a second ball is selected at random. What is the probability
that:
1. The sum of two balls is below five.
2. Both balls have odd numbers.
3. Two consecutive numbers ar chosen, in ascending order

The local lottery is found by randomly selecting 6 ping pong
balls from a container in order without replacement. There are 30
ping-pong balls in the container numbered 0 through 29. 1.) What is
the probability you hold the winning ticket? 2.) How many tickets
should you buy to give yourself a 1% chance of winning the lottery?
A 10% chance? A 25% chance? A 50% chance? 3.) What is the
probability all 6 numbers are even? At least one...

Assume you have a group of ten ping-pong balls numbered from 1-10.
Let us define some events as follows:
Event A: A
randomly selected ball has an odd number on it
Event B: A
randomly selected ball has a multiple of 3 on it
Event C: A randomly selected ball has either a 5 or 8 on it
Answer
the following questions related to probability of the above
described events for a SINGLE trial:
a.
P(A) =
(Remember
this is...

Two balls are chosen randomly from an urn containing 5 black and
5 white balls. Suppose that we win $1 for each black ball selected
and we lose $1 for each white ball selected. Denote our winnings by
a random variable X.
(a) (4 points) Provide the probability distribution of X.
(b) (2 points) Using the result in (a), what is the probability
that 0 ≤ X ≤ 2?

Three balls are randomly chosen from an urn containing 3 white,
4 red and 5 black balls. Suppose one will win $1 for each white
ball selected, lose 1$ for each red ball selected and receive
nothing for each black ball selected. Let Random Variable X denote
the total winnings from the experiment. Find E(X).

Two balls are chosen randomly from an urn containing 9 yellow, 5
blue, and 3 magenta balls. Suppose that we win $3 for each blue
ball selected, we lose $2 for each yellow ball selected and we win
$0 for each magenta ball selected. Let X denote our winnings. What
are the possible values of X, what are the probabilities associated
with each value (i.e., find the probability mass function of X),
and what is the expectation value of X,E[X]?

Two balls are chosen randomly from an urn containing 6 red and 4
black balls, without replacement. Suppose that we win $2 for each
black ball selected and we lose $1 for each red ball selected. Let
X denote the amount on money we won or lost.
(a) Find the probability mass function of X, i.e., ﬁnd P(X = k) for
all possible values of k.
(b) Compute E[X].
(c) Compute Var(X)

Let a ball be drawn from an urn containing four balls, numbered
1, 2, 3, 4, and all four outcomes are assumed equally likely. Let E
= {1, 2}, F = {1, 3}, G = {1, 4}, whether E, F, G are independent
with each other?

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