Question
In: Statistics and Probability
An urn contains three blue and seven green marbles. Alice chooses two marbles at random from...
An urn contains three blue and seven green marbles. Alice chooses two marbles at random
from the urn. If they have the same color, Bob will pay her $7; but if they have different colors, Alice will pay Bob $8
a) Give the probability distribution for Alice’s payoffs of this game. Use proper headings for the table.
b) What are Alice expected winnings in this game?
Is it a fair game?
Solutions
orchestra answered 2 years agoRelated Solutions
An urn contains 4 marbles, either blue or green. The number of blue marbles is equally...
An urn contains 4 marbles, either blue or green. The number of
blue marbles is equally likely to be 0, 1, 2, 3, or 4. Suppose we
do 3 random draws with replacement, and the observed sequence is:
blue, green, blue. What is the probability the urn contains just 1
blue marble?
An urn contains 4 marbles, either blue or green. The number of blue marbles is equally...
An urn contains 4 marbles, either blue or green. The number of
blue marbles is equally likely to be 0, 1, 2, 3, or 4. Suppose we
do 3 random draws with replacement, and the observed sequence is:
blue, green, blue. What is the probability the urn contains just 1
blue marble?
An urn has marbles of red, blue, and yellow. There are seven marbles of each of...
An urn has marbles of red, blue, and yellow. There are seven
marbles of each of the three colors. The experiment consists of
drawing a single, random marble from the urn. Define a random
variable X by
X(s) = -1 if the marble has red
0, if the marble has blue
+1, if the marble has yellow
54 random samples of X are taken. Approximate the probability
that the mean of the sample is between 0 and 1/20.
A bag contains one red marble, two blue marbles and three green marbles. A marble is...
A bag contains one red marble, two blue marbles and three green
marbles. A marble is selected at random. Define a random variable X
such that X=1 if a red marble is selected, X=2 if a blue marble is
selected and X=3 if a green marble is selected. Find the following
probabilities. Hint: The blue marbles are different; you can label
one blue-1 and the other blue-2. Similarly, each of the green
marbles is different.
4a) Find P(X=1)
4b) Find...
Experiment: An urn contains 4 blue marbles and 8 orange marbles. Two marbles are drawn without...
Experiment: An urn contains 4 blue marbles and 8 orange marbles.
Two marbles are drawn without replacement. What is the probability
that a blue and orange marble are drawn? A) 0.4444 B) 0.2424 C)
0.1212 D) 0.4848 E) 0.2222
The answer is D I just don't understand how my professor got
it.
A box contains 5 green marbles, 8 blue marbles, and 8 red marbles. Three marbles are...
A box contains 5 green marbles, 8 blue marbles, and 8 red
marbles.
Three marbles are selected at random from the box, one at a
time, without replacement.
Find the probability that the first two marbles selected are not
red, and the last marble is red.
A bag of marbles contains 3 blue marbles, 2 green marbles. 2 marbles are selected from...
A bag of marbles contains 3 blue marbles, 2 green marbles. 2
marbles are selected from the bag without replacement. What is the
probability of getting 1 green marble?
13) A box contains 5 green marbles, 6 blue marbles, and 8 red marbles. Three marbles...
13) A box contains 5 green marbles, 6 blue marbles, and 8 red
marbles. Three marbles are selected at random from the box, one at
a time, without replacement. Find the probability that the first
two marbles selected are not red, and the last marble is red. Round
your answer to four decimal places.
1 An urn contains three green chips and four blue chips. Two chips are removed is...
1 An urn contains three green chips and four blue chips. Two
chips are removed is succession. What is the probability both are
blue if:
a.) The chips are sampled with replacement?
b.) The chips are sampled without replacement?
2 An urn contains 5 orange and 4 red balls. Three balls are
removed. Lex R be the random variable (R.V.) denoting the number of
red balls in the sample of three balls. What is the probability two
of the balls...
A jar contains 4 Orange, 3 Blue, and 2 Green marbles. (a) Two marbles are selected...
A jar contains 4 Orange, 3 Blue, and 2 Green marbles.
(a) Two marbles are selected one at a time at random without
replacement, so order is observed in the sample. Define the
events:A=“the first marble is Orange”, B= “the second marble is
Orange”. Find(i)P(A), (ii)P(B), (iii)P(A∪B) =P(at least one Orange
marble is obtained in the 2 draws).
Show your work.
(b) Suppose instead three marbles are chosen at random from the
jar by choosing 3 in one hand; no...
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