Bag A contains 3 white and 2 red balls. Bag B contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from bag A and put into bag B. However if tail appears then 2 balls are drawn at random from bag A and put into bag B. Now one ball is drawn at random from bag B. Given that the drawn ball from B is white, the probability that head appeared on the coin is

$$ \text { If } P(B)=\frac{3}{5} \quad P(A / B)=\frac{1}{2} \text { and } P(A \cup B)=\frac{4}{5} \text { then } P(A \cup B)^{\prime}+P\left(A^{\prime} \cup B\right)= $$

The probability distribution of a discrete random variable X is given as

$$ \text { Then the value of } A \text { if } E(X)=2.94 \text { is } $$

18 Points are indicated on the perimeter of a triangle $$\mathrm{ABC}$$ as shown below. If three points are chosen then probability that it will from a triangle is