Question

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.)

Answer #1

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...

An urn contains 9 red balls, 7 blue balls and 6 green
balls. A ball is selected and its color is noted then it is placed
back to the urn. A second ball is selected and its color is noted.
Find the probability that the color of one of the balls is red and
the color of the other ball is blue.
A. 0.2603
B. 0.2727
C. 0.4091
D. 0.3430

Question2.
An urn initially contains r red balls and b blue balls. In each
step, a ball is chosen uniformly at random, and then put back into
the urn together with a new ball of the same color. Let Ri be the
event that in step i a red ball is chosen from the urn. Show that
P(R1 ∩ R2) = P(R2 ∩ R3).

An urn contains 7 red balls, 18 blue balls and 15
green balls. A ball is selected and its color is noted and then it
is placed back to the urn. A second ball is selected and its color
is noted. Find the probability of that both balls has the same
color.
A. 0.1575
B. 0.3738
C. 0.3750
D. 0.1750

Urn A contains two red balls and eight blue balls. Urn B
contains two red balls and ten green balls. Six balls are drawn
from urn A and four are drawn from urn B; in each case, each ball
is replaced before the next one is drawn. What is the most likely
number of blue balls to be drawn? What is the most likely number of
green balls to be drawn?

Suppose that:
Urn U1 contains 3 blue balls and six red balls, and
Urn U2 contains 5 blue ball and 4 red balls
Suppose we draw one ball at random from each urn. If the two
balls drawn have different colors, what is the probability that the
blue ball came from urn U1?

An urn contains 10 balls, 2 red, 5 blue, and 3 green balls. Take
out 3 balls at a random,
without replacement. You win $2 for each green ball you select and
lose $3 for each red ball you
select. Let the random variable X denote the amount you win,
determine the probability mass
function of X.

An urn contains 4 red balls and 6 green balls. Three balls are
chosen randomly from the urn, without replacement. (a) What is the
probability that all three balls are red? (Round your answer to
four decimal places.) (b) Suppose that you win $50 for each red
ball drawn and you lose $25 for each green ball drawn. Compute the
expected value of your winnings.

An urn contains 6 green ball, 7 blue balls and 5 yellow balls.
You are asked to draw 3 balls, one at a time (without replacement).
Find the probability that a green is pulled first, then another
green ball then a blue ball.

Refer to Example 4.40. An urn contains eight red balls, eight
white balls, and eight blue balls, and sample of five balls is
drawn at random without replacement.
Compute the probability that the sample contains at least one ball
of each color. (Round your answer to four decimal places.)

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