What is the Probability of Drawing a White Ball from the Second Urn?

In summary, the probability of picking a white ball from the second urn after 2 balls are drawn from the first urn and placed in it is 59/130.
  • #1
Debdut
19
2
An urn contains 10 white and 3 black balls. Another urn contains 3 white and 5 black balls. 2 balls are drawn at random from the first urn and placed in the second urn and 1 ball is drawn at random from the second urn. What is the probability that it is white?

Is the answer 59/130
 
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  • #2
Please tell us why you think that.
 
  • #3
Check your arithmetic debdut.
 
  • #4
xiavatar said:
Check your arithmetic debdut.

I also get 59/130. Nevertheless, the OP should show his/her work.
 
  • #5
I don't know whether I have done it correctly or not...

There are 4 combinations of picking 2 balls from 1st urn (White → W, Black → B)

WW → P = 10/13 x 9/12 = 15/26
BB → P = 3/13 x 2/12 = 1/26
WB → P = 10/13 x 3/12 = 5/26
BW → P = 3/13 x 10/12 = 5/26

If WW was picked, then balls in 2nd urn = 5W 5B, Then probability of picking white ball = 5/10
If BB was picked, then balls in 2nd urn = 3W 7B, Then probability of picking white ball = 3/10
If WB was picked, then balls in 2nd urn = 4W 6B, Then probability of picking white ball = 4/10
If BW was picked, then balls in 2nd urn = 4W 6B, Then probability of picking white ball = 4/10

Thus total probability of picking white ball from 2nd urn = (5/10 x 15/26)+(3/10 x 1/26)+(4/10 x 5/26)+(4/10 x 5/26) = 59/130
 
  • #6
Yes, that is correct.
 

FAQ: What is the Probability of Drawing a White Ball from the Second Urn?

1. What is "Probability Problem"?

Probability problem is a mathematical question that involves calculating the likelihood of a certain event occurring. It is a branch of mathematics that deals with the study of random phenomena and uncertainty.

2. How is probability calculated?

Probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This can be represented as a fraction, decimal, or percentage.

3. What is the difference between theoretical and experimental probability?

Theoretical probability is the likelihood of an event occurring based on mathematical calculations and assumptions. It is often used in theoretical models and does not require actual data. Experimental probability, on the other hand, is based on actual data and is calculated by conducting experiments or observations.

4. How is probability used in real life?

Probability is used in many real-life situations, such as in weather forecasting, gambling, insurance, and medical research. It helps us make predictions and informed decisions based on the likelihood of certain events occurring.

5. Can probability be greater than 1 or less than 0?

No, probability cannot be greater than 1 or less than 0. A probability of 1 means that an event is certain to occur, while a probability of 0 means that it is impossible for the event to occur. All probabilities must fall between 0 and 1, inclusive.

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