An urn contains 7 white and 5 black balls.

Question

An urn contains 7 white and 5 black balls. A ball is drawn at random and is put back into the urn along with 3 additional balls of the same colour as that of the ball drawn. A ball is again drawn at random. Then the probability that the ball drawn is white is

Smart Achievers · Accepted Answer

(3)

$W_{1} = ball drawn in the first draw is white$

$W_{2} = ball drawn in the second draw is white,$ $P (W_{1}) = \frac{7}{12}$

$P (B_{1}) = \frac{5}{12},$ $P (W_{2} / W_{1}) = \frac{10}{15},$ $P (W_{2} / B_{1}) = \frac{7}{15}$

$P (W_{2}) = P (W_{1}) \times P (W_{2} / W_{1}) + P (B_{1}) \times P (W_{2} / B_{1})$

Solution

Q.
An urn contains 7 white and 5 black balls. A ball is drawn at random and is put back into the urn along with 3 additional balls of the same colour as that of the ball drawn. A ball is again drawn at random. Then the probability that the ball drawn is white is

1 $\frac{7}{32}$

2 $\frac{5}{12}$

3 $\frac{7}{12}$

4 $\frac{10}{25}$

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Solution

Q. An urn contains 7 white and 5 black balls. A ball is drawn at random and is put back into the urn along with 3 additional balls of the same colour as that of the ball drawn. A ball is again drawn at random. Then the probability that the ball drawn is white is

1 732

2 512

3 712

4 1025