Question

4 In calculating the probability of losing a game, you told a friend that your textbook referred to a loss as “favorable event.” Your friend challenged you and said that a loss is not favorable. What would you say in response?

Answer #1

Favorable outcome has nothing to do with losing or winning. It can be any event in which we are interesting.

Suppose we want to find the probability of dancing out of swimming, running, walking, jumping and dancing.

Here favorable outcome is dancing because we are interested in dancing event.

If we want to find the probability of running, then running will be our favorable event.

So, favorable outcome can be negative, positive, winning or losing, etc.

Suppose you play a game with a friend and the probability of
losing is 6/11 The odds against losing would be

3. A friend said that he was told that the expected value of a
game was $1.00, but he played twice and lost $1.50. He said he must
have been told a lie. How would you respond? Exercise 25 in Section
5.5 is relevant to this topic. What does it mean to say that a game
is fair? Does it mean that you can never lose money? Exercise 18 in
Section 5.5 is relevant to this topic.

Suppose that you and your friend alternately play a game. Both
of your and your friend’s chance of winning in each game is 0.5.
All the outcomes are independent. Each of you will play 100 games.
Estimate the probability that you will win at least 5 more games
than your friend. Both Y and Z follows Bin(100, 0.5). Y = number of
games you win Z = number of games your friend wins.

Suppose that you and your friend alternately play a game. Both
of your and your friend’s chance of winning in each game is 0.5.
All the outcomes are independent. Each of you will play 100
games.
Estimate the probability that you will win at least 5 more games
than your friend.
Both Y and Z follows Bin(100, 0.5).
Y = number of games you win
Z = number of games your friend wins.

You and a friend are rolling a set of 7 dice. The game works
such that if a die shows the values 1, 2, 3, or 4 you will get a
point for that die. Each die that shows 5 or 6 your friend will get
a point for.
Construct a probability model for a single roll of the dice then
answer the following.
A)What is the probability you made 2 points?
B)What is the probability that your friend will...

You and a friend are rolling a set of 5 dice. The game works
such that if a die shows the values 1, 2, 3, or 4 you will get a
point for that die. Each die that shows 5 or 6 your friend will get
a point for. Construct a probability model for a single roll of the
dice then answer the following.
Step 1 of 5:
What is the probability you made 2 points?
Step 2 of 5:...

You and a friend are rolling a set of 6 dice. The game works
such that if a die shows the values 1, 2, or 3 you will get a point
for that die. Each die that shows 4, 5, or 6 your friend will get a
point for.
Construct a probability model for a single roll of the dice then
answer the following.
Step 1 of 5:
What is the probability you made 2 points?
Step 2 of 5:...

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...

Your friend asks you to play a gambling game. If you give her $1,
you get to roll two dice. If you get a total of 11 or 12, she will
give you a $5 bill. If your total is 7 she will give back your $1.
Otherwise she keeps your $1. Let X be your overall gain after one
round.
a) Construct the probability distributio table for X.
b) Compute E(X).
c) If you started with $1000, how much...

You were told that the average number of calories in a
low-calorie meal is 450. Your friend started
making low calorie meals at her restaurant. You took a
sample of 27 such meals and the mean for these meals is 440 and the
standard deviation is 22 calories. You want to
test the hypothesis that the average for this sample is different
from the national average, your friend told you that she is sure
that her meals have fewer calories. Do the test
again. Use...

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