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555-605 Level|   Probability|      
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An urn contains four white and five black balls, a second urn contains 08 Jan 2021, 11:29
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C
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An urn contains four white and five black balls, a second urn contains five white and four black balls. One ball is transferred from the first to the second urn, then a ball is drawn from the second urn. What the probability that it is white?

A. 41/90
B. 19/42
C. 49/90
D. 17/30
E. 19/21


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C
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An urn contains four white and five black balls, a second urn contains 08 Jan 2021, 12:49
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The chance of a white ball to be picked from the 1st urn is 4/9 which would result a 6/10 chance a white ball to be picked from the 2nd. Together the chance of that is 24/90.

The chance of a black ball to be picked from the 1st urn is 5/9 which would result a 5/10 chance a white ball to be picked from the 2nd. Together the chance of that is 25/90.

Since these two conditions are mutually exclusive, you should add them and get answer C.
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An urn contains four white and five black balls, a second urn contains 09 Jan 2021, 12:07
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Given, Urn 1: w= 4 and B= 5. Urn2: w=5 and B=4

One ball is moved from urn 1 to 2 and then 1 ball is selected form urn 2. So, between urn 1 and 2, there is a dependent event and selection of from urn 2 is independent events.

Case 1: When a White ball is moved from urn 1. P(E1) = 4C1/9C1 * 6C1/10C1 =24/90
Case 2: When a Black ball is moved from urn 1. P(E2) = 5C1/9C1 * 5C1/10C1 =25/90

P(E) = P(E1) + P(E2) = 24/90 + 25/90 = 49/90. So, I think C. :)
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An urn contains four white and five black balls, a second urn contains 19 Jan 2021, 10:14
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Bunuel
An urn contains four white and five black balls, a second urn contains five white and four black balls. One ball is transferred from the first to the second urn, then a ball is drawn from the second urn. What the probability that it is white?

A. 41/90
B. 19/42
C. 49/90
D. 17/30
E. 19/21


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Solution:

If a white ball is transferred from the first urn to the second given that there is a 4/9 chance of doing so, then there will be 6 white balls (out of 10 balls) in the second urn. Thus, the probability of selecting a white ball from the second urn after a white ball is transferred is 4/9 x 6/10 = 24/90.

If a black ball is transferred from the first urn to the second given that there is a 5/9 chance of doing so, then there will be 5 white balls (out of 10 balls) in the second urn. Thus, the probability of selecting a white ball from the second urn after a black ball is transferred is 5/9 x 5/10 = 25/90.

Therefore, the probability of selecting a white from the second urn after a ball (white or black) is transferred is 24/90 + 25/90 = 49/90.

Answer: C
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An urn contains four white and five black balls, a second urn contains 19 Jan 2021, 23:40
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Urn 1: White = 4 and Black = 5

Urn 2: White = 5 and Black = 4

One ball is transferred from the first to the second urn, then a ball is drawn from the second urn: The ball transferred can be a white or a black.

Case I: White ball transferred : Probability to pick white ball from Urn 1: \(\frac{4}{9}\)

Urn 2: White = 6 and Black = 4

Total: 6 + 4 = 10

Probability of white: \(\frac{4}{9}\) * \(\frac{6}{10}\) = \(\frac{24}{90}\)

Case II: Black ball transferred: Probability to pick a black ball from Urn 1: \(\frac{5}{9}\)

Urn 2: White = 5 and Black = 5

Total: 5 + 5 = 10

Probability of white: \(\frac{5}{9}\) * \(\frac{5}{10}\) = \(\frac{25}{90}\)

Overall probability: \(\frac{24}{90}\) + \(\frac{25}{90}\) = \(\frac{49}{90}\)

Answer C
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An urn contains four white and five black balls, a second urn contains 20 May 2024, 12:01
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