Question

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.

Answer #1

total number of balls= 6+7+5 = 18

we know

for first draw total outcome is 18 . number of green ball is 6 . so probabilty to take green ball in first draw is

for second draw total outcome becomes 17 (with out replacement) . here number of green ball will be 5 . so probability to take green ball in second draw is

for third draw , total outcome is 16 . number of blue ball is 7 . so probabilty to take blue ball in third draw is

so probablity for this complete drawing is

**so answer is 0.043 .**

**if exact answer is needed then answer is fraction
35/816**

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

An urn contains 7 blue and 8 green balls. You remove 3 balls
from the urn without replacement. What is the probability that at
least 2 out of the 3 balls are green.

An urn contains 10 red balls, 7 green balls, and 3 yellow balls.
Draw 5 balls.
What's the probability that you draw 2 red, 2 green, and 1
yellow?
(Same experiment as above) What's the probability that you draw
2 red, 1 green, and 2 yellow?

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.)

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

An urn contains 1 green ball, 1 red ball, 1 yellow ball and 1
white ball. I draw 5 balls with replacement. What is the
probability that exactly 2 balls are of the same color?

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 three red balls, two blue balls and one yellow
ball. Our experiment is to draw a ball from an urn, replace it, and
draw another. Define a random variable δ: Ω → R by δ(ω) = 1 if you
draw the same color twice in a row, and δ(ω) = 0 otherwise. What is
the expected value of δ?

Urn A contains 6 green and 4 red balls, and Urn B contains 3
green and 7 red balls. One ball is drawn from Urn A and transferred
to Urn B. Then one ball is drawn from Urn B and transferred to Urn
A. Let X = the number of green balls in Urn A after this process.
List the possible values for X and then find the entire probability
distribution for X.

2. Urn A contains 6 green and 4 red balls, and Urn B contains 3
green and 7 red balls. One ball is drawn from Urn A and transferred
to Urn B. Then one ball is drawn from Urn B and transferred to Urn
A. Let X = the number of green balls in Urn A after this process.
List the possible values for X and then find the entire probability
distribution for X.

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