Question

There are two urns. The first urn has three red, one blue and four yellow marbles. The second urn has two red, four blue and two yellow marbles. If you draw one marble from each urn, what are the probabilities of the following events?

What is the chance of getting two blue marbles?

What is the chance of getting no blue marbles?

What is the chance of getting at least one yellow marble?

What is the chance that the marbles will not be the same color?

What is the chance of getting one red marble and one yellow marble?

Suppose I draw two marbles from urn 1, ignoring urn 2. The draws are without replacement. What is the probability of getting two yellow marbles?

Now suppose only one marble is drawn, and you don't know which urn it was drawn from. The marble is blue. Use Bayes' theorem to determine the probability that it was drawn from urn 2.

Answer #1

A bag contains three red marbles, one yellow marble, and six
green marbles. Two marbles are drawn from the bag with replacement.
One marble is drawn, the color is recorded, and the marble is
returned to the bag. A second marble is drawn from the bag and the
color is recorded.
a. What is the probability that both marbles are yellow?
b. What is the probability that both marbles are red?
c. What is the probability of drawing one green...

urn
A contains 5 red marbles and 1 yellow marble. Urn b contains of 3
red marbles and 7 yellow marbles. A marble is selected at random
from urn A and put aside. If the marble is res, the. two marbles
are selecred at random from Urn B (no replacements). If the marble
is yellow, then three marbles are selected at random from Urn b (no
replacement)
(a) what is the probability if selecting exaclty one yellow
marble from urn...

Urn 1 contains 8 red and 6 Blue marbles and Urn 2 contains 5 red
marbles and 4 blue marbles. A marble is randomly selected from Urn
1 and Placed in Urn 2. A marble is then drawn from Urn 2
a. What is the probability that the marble drawn from Urn 2 is
red?
b. What is the conditional probability that the ball drawn from
Urn 1 is red, given that a blue marble is drawn from Urn 2?

A bag contains 8 blue marbles, 3 red marbles, 7 yellow marbles.
If one marble is drawn from the bag then replaced, what is the
probability of drawing a blue marble then a yellow marble?
In a number guessing game. You ask a person to guess a number
from one 1 to 10. If the person makes a random guess, what is the
probability their guess will be less than 3?
A bag contains 3 white marbles, 7 yellow marbles,...

1. A bag contains one green marble, two yellow marbles, four
blue marbles, and five red marbles.
a. What is the theoretical probability of randomly drawing a
blue marble from the bag?
b. If you triple the number of green, yellow, blue, and red
marbles in the bag, what will be the theoretical probability of
drawing a blue marble?
C. Compare your answers for part (a) and (b). Are they the same
or different? Explain.
d. How many blue marbles...

In an urn, there are 20 balls of four colors: red, black, yellow
and blue. For each color, there are 5 balls and they are numbered
from 1 to 5.
1) If one ball is randomly drawn from the urn, what is the
probability that the randomly selected ball is red or blue?
2) If one ball is randomly drawn from the urn, what is the
probability that the randomly selected ball is numbered 1 or
blue?

1. An urn contains two red, one purple, and two green marbles.
Two marbles are randomly drawn in succession without replacement.
Determine the probability that the first marble is green and the
second is red.
2. An urn contains two red, two purple, and two green marbles.
Two marbles are randomly drawn in succession
without replacement. Determine the probability
that both marbles are red.

Four marbles are being drawn from an urn containing 8 blue and 2
red marbles. Let X be
the number of blue marbles drawn.
(a) (6 pts) What this the probability mass function for X if the
marbles are drawn with replacement.
(b) (6 pts) Compute E[X] in this case?
(c) (6 pts) Suppose now the four marbles were drawn without
replacement. Find the prob- ability mass function.
(d) (6 pts) Compute E[X] in this case.

A bag contains 3 red marbles, 5 blue marbles, 8 yellow marbles,
and 7 green marbles. What is the probability of choosing a yellow
or green marble when one marble is drawn?

A bag contains 3 red marbles, 5 blue marbles, 8 yellow marbles,
and 7 green marbles. What is the probability of choosing a yellow
or green marble when one marble is drawn?

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