SOLUTION: An urn contains 3 white balls and 7 red balls. A second urn contains 8 white balls and 2 red balls. An urn is selected, and the probability of selecting the first urn is 0.2. A bal

Question 1203812: An urn contains 3 white balls and 7 red balls. A second urn contains 8 white balls and 2 red balls. An urn is selected, and the probability of selecting the first urn is 0.2. A ball is drawn from the selected urn and replaced. Then another ball is drawn and replaced from the same urn. If both balls are white, what are the following probabilities? (Round your answers to three decimal places.)
(a) the probability that the urn selected was the first one

(b) the probability that the urn selected was the second one

Answer by ikleyn(52778) (Show Source): You can put this solution on YOUR website!
.
An urn contains 3 white balls and 7 red balls. A second urn contains 8 white balls and 2 red balls.
An urn is selected, and the probability of selecting the first urn is 0.2.
A ball is drawn from the selected urn and replaced.
Then another ball is drawn and replaced from the same urn.
If both balls are white, what are the following probabilities?
(Round your answers to three decimal places.)
(a) the probability that the urn selected was the first one
(b) the probability that the urn selected was the second one
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Both questions (both parts) are about calculating a conditional probability.

(a)  This conditional probability is the fraction, whose denominator is the probability
     to get white balls in the first and the second drawn from ANY of the TWO urns, 
     while the numerator is the probability to get white balls in the first and the second drawn 
     from the FIRST urn.

     Keeping it in mind, we write the formula immediately

         P =  =  = 0.034  (rounded as requested).    ANSWER



(b)  This conditional probability is the fraction, whose denominator is the probability
     to get white balls in the first and the second drawn from ANY of the TWO urns, 
     while the numerator is the probability to get white balls in the first and the second drawn 
     from the SECOND urn.

     Keeping it in mind, we write the formula immediately

         P =  =  = 0.966  (rounded as requested).    ANSWER

Solved.

RELATED QUESTIONS
An urn contains 4 white balls and 6 red balls. A second urn contains 6 white balls and 4... (answered by greenestamps,math_tutor2020)

An urn contains 3 white balls and 7 red balls. A second urn contains 8 white balls and 2... (answered by ikleyn,math_tutor2020)

Urn 1 contains 6 red balls and 5 black balls. Urn 2 contains 3 red balls and 3 black... (answered by Boreal)

There are three urns that each contain 10 balls. The first contains 3 white balls and 7... (answered by scott8148)

An urn contains 3 red and 2 white numbered balls. A sample of 2 balls is randomly chosen. (answered by stanbon)

Urn 1 contains 7 red balls and 4 black balls. Urn 2 contains 4 red balls and 1 black... (answered by math_helper,ikleyn)

Urn 1 contains 3 red balls and 2 black balls. Urn 2 contains 2 red balls and 2 black... (answered by ikleyn)

Urn 1 contains 3 red balls and 4 black balls. Urn 2 contains 4 red balls and 2 black... (answered by jim_thompson5910)

An urn contains 8 white balls and 4 red balls. In how many ways can 4 balls be drawn if... (answered by stanbon)