Question

A bag has 3 red and 7 white balls. One ball is drawn from the bag and it is replaced by ball of other colour, then one ball is taken from the bag. Find the probability that the second ball is red

Answer 1

Answer:

The probability can be 2/10 or 3/10

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Answer 2

Answer:

For the first draw,

the probability of getting red ball is 3/(7+3)

i.e. 3/10

probability of getting a white ball is 7/(7+3)

i.e. 7/10

Now let's say the ball drawn was white.

Then the replaced ball will be red.

Hence the count is 4 red and 6 white

hence the probability of picking a red ball now is 4/(4+6)

i.e 4/10 or 2/5. (i)

Now let's say the ball drawn was red.

Then the replaced ball will be white.

Hence the count is 2 red and 8 white.

Therefore the probability of picking a red ball now is 2/(2+8)

i.e 2/10 or 1/5. (ii)

Now the probability of case (i) is 7/10 and the probability of case (ii) is 3/10

therefore the final answer will be

(7/10 * 2/5 ) + (3/10 * 1/5)

which gives

(14/50) + (3/50)

which is

17/50