Question

2. Katie bets $1 on a 2-digit number. She wins $75 is she draws her number from the set of all 2-digit numbers, {00,01,02,...,99}; otherwise, she loses her $1.

(a) [5 pts] What is the probability that Katie wins? If she wins, what is the payoff ?

(b) [5 pts] What is the probability that Katie loses? If she loses, what amount is the loss?

(c) [6 pts] How do you use the information in parts a and b to find the expected value for this game? (d) [4 pts] Is this game fair, favorable, or unfavorable to Katie? Explain your answer based on the expected value you found in part c.

Answer #1

A person has $32. The person decides to play roulette. She
always bets on Red. (To simplify the problem assume that P(Red) =
.5)
a) Let X be the random variable for the amount that she makes if
she bets $8 on each roll and does this for four rolls. What is the
probability function for X? What is E(X)?
b) Let Y be the amount that she makes if she follows the
following strategy.
She bets $1 on roll...

In a game of “Chuck a luck” a player bets on one of the numbers
1 to 6. Three dice are then rolled and if the number bet by the
player appears i times (where i equals to 1, 2 or 3) the player
then wins i units. On the other hand if the number bet by the
player does not appear on any of the dice the player loses 1 unit.
If x is the players’ winnings in the...

In a game of “Chuck a luck” a player bets on one of the numbers
1 to 6. Three dice are then rolled and if the number bet by the
player appears i times (where i equals to 1, 2 or
3) the player then wins i units. On the other hand if the
number bet by the player does not appear on any of the dice the
player loses 1 unit. If x is the players’ winnings in the...

A gambler plays a dice game where a pair of fair dice are rolled
one time and the sum is recorded. The gambler will continue to
place $2 bets that the sum is 6, 7, 8, or 9 until she has won 7 of
these bets. That is, each time the dice are rolled, she wins $2 if
the sum is 6, 7, 8, or 9 and she loses $2 each time the sum is not
6, 7, 8, or...

You play the following game against your friend. You have 2 urns
and 4 balls One of the balls is black and the other 3 are white.
You can place the balls in the urns any way that you'd like,
including leaving an urn empty. Your friend will choose one urn at
random and then draw a ball from that urn. ( If he chooses an empty
urn, he draws nothing.) She wins if she draws the black ball and...

A brilliant young golfer wins 15% of the tournaments she enters.
We will assume the results of each tournament are independent of
other tournaments. a) If she enters 20 tournaments this year, what
is the probability she will win none of them? b) What is the
expected value of the number of tournaments she must enter in order
to win her first tournament? What is the variance of that
number?

A lottery game called Pick 5 where the player pays $1 and picks
a 5-digit number. If the 5 numbers come up in the order you picked,
then you win $3,000. What is your expected value?

A lottery game called Pick 5 where the player pays $1 and picks
a 5-digit number. If the 5 numbers come up in the order you picked,
then you win $3,000. What is your expected value?

The game requires $5 to play, once the player is admitted, he
or she has the opportunity to take a chance with luck and pick from
the bag. If the player receives a M&M, the player loses. If the
player wins a Reese’s Pieces candy, the player wins. If the player
wins they may roll a dice for a second turn, if the die rolls on a
even number, they may pick from the bag once again with no extra...

If layne is a 75% free-throw shooter, A)what is the
probability that she makes exactly 3 of the 5 shots that she takes
in the game?
B) what is the probability that she misses 2 of the 5 shots that
she takes in the game?
using the information above about Laynes free-throw
shooting ability. Assume that Layne is a 43% 3-point shooter. your
team is ahead by 2 points with less than a second on the clock and
Layne is...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 6 minutes ago

asked 12 minutes ago

asked 14 minutes ago

asked 26 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago