Question

Can someone please answer these two questions by Friday?

Problem 1 An urn contains 10 red and 5 black and 3 green balls. Two balls are picked (one after the other) from the urn. Given that the second ball is red, find the probability that the first was green.

Problem 2 Charles is taking a multiple choice probability exam, and for each question, there are 3 possible answers, out of which only one is correct. Since the time is short, for any question, with probability 3/4 Charles decides to do the calculations and with probability 1/4 he just choses one of the 3 answers randomly. Whenever he decides to do the calculations, with probability 4/5 he will get the correct answer and with probability 1/5, he gets an answer which matches one of the 2 wrong answers. Suppose that he got a particular question wrong. What is the probability he actually did the calculations?

Answer #1

P(2nd ball was red) =P(1st green and 2nd red)+P(1st red and 2nd red)+P(1st black and 2nd red)

=(3/18)*(10/17)+(10/18)*(9/17)+(5/18)*(10/17)=5/9

P( first was green given 2nd ball was red )=P(1st green and 2nd red)/P(2nd ball was red)

=(3/18)*(10/17)/(5/9)=3/17

2)

P(got it right) =P(do the calculation and got it right)+P(not do the calculation and do it right)

=(3/4)*(4/5)+(1/4)*(1/3)=41/60

therefore P( did the calculations |got it right)

=P(do the calculation and got it right)/P(got it right)

=(3/4)*(4/5)/(41/60)

=36/41

Urn A contains 5 green and 4 red balls, and Urn B contains 3
green and 6 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.

One urn contains 10 red balls and 10 white balls, a second urn
contains 8 red balls and 4 white balls, and a third urn contains 5
red balls and 10 white balls. An urn is selected at random, and a
ball is chosen from the urn. If the chosen ball is white, what is
the probability that it came from the third urn? Justify your
answer.

Urn A contains 5 green and 3 red balls, and Urn B contains 2
green and 6 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.

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.

Urn 1 contains 4 red balls and 3 black balls. Urn 2 contains 1
red ball and 3 black balls. Urn 3 contains 4 red balls and 2
black balls. If an urn is selected at random and a ball is
drawn, find the probability that it will be red.
Enter your answer as a fraction in simplest form or a decimal
rounded to 3 decimal places.
P(red)=

Urn 1 contains 7 red balls and 3 black balls. Urn 2 contains 4
red balls and 1 black ball. Urn 3 contains 4 red balls and 3 black
balls. If an urn is selected at random and a ball is drawn, find
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enter your answer as a decimal rounded to 3 decimal places

Urn A has 8 Red balls and 5 Green balls while Urn B has 1 Red
ball and 3 Green balls.
A fair die is tossed. If a “5” or a “6” are rolled, a ball is drawn
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(a) Determine the conditional probability that the chosen ball is
Red given that Urn A is selected?
(b) Determine the conditional probability that the chosen ball is
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Urn 1 contains 7 red balls and 3 black balls. Urn 2 contains 1
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ball. If an urn is selected at random and a ball is drawn, find the
probability that it will be red.
Enter your answer as a fraction in simplest form or a decimal
rounded to 3 decimal places.

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
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(Same experiment as above) What's the probability that you draw
2 red, 1 green, and 2 yellow?

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