probability

earth@work wrote:probability
An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red?
Ans: 1/2

Probability of picking red ball = 5/10 = 1/2
Probability of picking black ball = 5/10 = 1/2

This question states that balls are picked with replacement.

Therefore, probability of picking red ball second time or third time or fourth time will always be 1/2.

This is more like a coin flip question.

What is the probability of getting heads in the second toss = 1/2

Hope this helps. Let me know if I am missing something.

There are two cases :
Case I : When the first drawn ball is a black one.

In this case the probability of drawing a black ball when there are 5 red and 5 black=5/10
And the probability of drawing a red ball when two more black balls are being added = 5/12
Hence total probability in this case = (5/10)*(5/12)

Case II : When the first drawn ball is red one.
In this case the probability of drawing a red ball when there are 5 red and 5 black=5/10
And the probability of drawing a red ball when two more red balls are being added = 7/12
Hence total probability in this case = (5/10)*(7/12)


Therefore the net probability from two cases =(5/10)*(5/12) +(5/10)*(7/12)

=1/2

thanks a lot