A bag initially contains I red and 2 blue balls. An experiment consisting of selecting a ball at random, noticing its colour and replacing it together with an additional ball of the same colour. If three such trails are made, then

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Probability that all the drawn balls are red given that all the drawn balls are of same colour is 0.2

Probability that at least one red ball is drawn is 0.6

Probability that exactly one blue ball is drawn is 0.2

Probability that at least one blue ball is drawn is 0.9

answer is A, B, C, D.

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Detailed Solution

$\begin{array}{l} P (E_{1}) = 1 - P (RRR) - 1 - [\frac{1}{3} \times \frac{2}{4} \times \frac{3}{5}] = 0 .9 \\ P (E_{2}) = 3 P (RRR) = 3 \times \frac{1}{2} \times \frac{1}{4} \times \frac{2}{5} = 0 .2 P (E_{3}) = P (RRR) (RRR \cup BBB) = \frac{P (RRR)}{P (RRR) + P (BBB)} = 0 .2 \end{array}$

$P (E_{4}) = 1 - P (B B B) = 1 - \frac{2}{5} = 0.6$

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