Two urns identical in appearance contain respectively $3$ green and $2$ black balls and $2$ green and $5$ black balls. One urn is selected at random and a ball is drawn from it. The probability that it is black is

For independent events $A$ and $B$,if $P(A) = p$,$P(B) = \frac{1}{2}$,and $P(A \cup B) = \frac{3}{5}$,then find the value of $p$.

$A$ bag contains $10$ similar balls,of which $4$ are blue and $6$ are red. Three balls are taken out at random from the bag one after the other without replacement. The probability that all the three balls drawn are red is

$A$ person has undertaken a construction job. The probabilities are $0.65$ that there will be a strike,$0.80$ that the construction job will be completed on time if there is no strike,and $0.32$ that the construction job will be completed on time if there is a strike. Determine the probability that the construction job will be completed on time.

Two marbles are drawn in succession from a box containing $10$ red,$30$ white,$20$ blue and $15$ orange marbles,with replacement being made after each drawing. Then the probability,that the first drawn marble is red and the second drawn marble is white,is

$A$ bag $X$ contains $2$ white and $3$ black balls,and another bag $Y$ contains $4$ white and $2$ black balls. If one bag is selected at random and one ball is drawn from it,what is the probability that the ball is white?