Question

- A bag contains three balls: one red, one yellow, and one blue.
Suppose you select two balls with replacement.
- Write the sample space for this procedure by listing out all the possible outcomes that could result.

- What is the probability that both balls you select are the same color?

________

- What is the probability you select at least one yellow ball?

________

Answer #1

A box contains one yellow, two red, and three green balls. Two
balls are randomly chosen without replacement. Define the following
events:
A:{ One of the balls is yellow }
B:{ At least one ball is red }
C:{ Both balls are green }
D:{ Both balls are of the same color }
Find the following conditional probabilities:
P(B\Ac)=
P(D\B)=

A box contains one yellow, two red, and three green balls. Two
balls are randomly chosen without replacement. Define the following
events:
A: \{ One of the balls is yellow \}
B: \{ At least one ball is red \}
C: \{ Both balls are green \}
D: \{ Both balls are of the same color \}
Find the following conditional probabilities: (a) P(B|D^c)
(b) P(D|C)
(c) P(A|B)

Consider a box containing 8 red, 10 blue and 12 yellow balls.
Draw three balls one by one with replacement. Then answer the
following questions:
a) Write down the sample space
b) Calculate the probability that there is at least one red
ball
c) What is the probability that the first two balls are red
d) Calculate the probability that the first two balls are red
given at least one ball is red?
e) What can you conclude based on...

A bag contains 10 white, 12 blue, 13 red, 7 yellow, and 8 green
wooded balls. A ball is selected from the bag, its color noted,
then replaced. You then draw a second ball, note its color and then
replace the ball. What is the probability of selecting 2 white
balls? Round to the nearest ten-thousandth.

Bag 1 contains six red balls, seven blue balls, and three
green balls. Bag 2 contains eight red balls, eight blue
balls, and two green balls. Bag 3 contains two red balls,
nine blue balls, and eight green balls. Bag 4 contains
four red balls, seven blue balls, and no green balls.
Bag 1 is chosen with a probability of 0.15, bag 2 with a
probability of 0.20, bag 3 with a probability of 0.35, and
bag 4 with a...

A bag contains blue and red balls. Two balls are drawn randomly
without replacement. The probability of selecting a blue and then a
red ball is 0.2. The probability of selecting a blue ball in the
first draw is 0.5. What is the probability of drawing a red ball,
given that the first ball drawn was blue?

One ball is chosen at random from a bag containing 12 red balls,
3 yellow balls, and 5 green balls.
i. If 1000 trials are completed (with replacement), about how
many times would you expect to select a red ball?
ii. If two balls are selected at random without replacement,
what is the probability that they are both red? Write your answer
as a decimal rounded to 3 decimal places.

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...

An urn contains five blue, six green and seven red balls. You
choose five balls at random from the urn, without replacement (so
you do not put a ball back in the urn after you pick it), what is
the probability that you chose at least one ball of each
color?(Hint: Consider the events: B, G, and R, denoting
respectively that there are no blue, no green and no red balls
chosen.)

Two balls are selected with replacement from an urn containing 7
red and 3 blue balls a. What is the probability that both balls are
red? b. What is the probability that both balls are blue? c. What
is the probability that the first ball is red and the second is
ball is blue? d. What is the probability that the first ball is
blue and the second ball is red? e. What is the probability that
the two balls...

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