$A$ bag $x$ contains $3$ white balls and $2$ black balls and another bag $y$ contains $2$ white balls and $4$ black balls. $A$ bag and a ball out of it are picked at random. The probability that the ball is white,is

An urn contains $10$ black and $5$ white balls. Two balls are drawn from the urn one after the other without replacement. What is the probability that both drawn balls are black?

If $A$ and $B$ are two independent events such that $P(A) = 0.40$ and $P(B) = 0.50$,find $P(\text{neither } A \text{ nor } B)$.

Two cards are drawn one by one at random from a pack of $52$ cards. The probability that both of them are king,is

Bag $A$ contains $4$ white and $2$ black balls,bag $B$ contains $3$ white and $3$ black balls,and bag $C$ contains $2$ white and $4$ black balls. If a bag is chosen at random and a ball is chosen at random from it,then the probability that the ball drawn is black is

Three groups $A, B, C$ are competing for positions on the Board of Directors of a company. The probabilities of their winning are $0.5, 0.3, 0.2$ respectively. If group $A$ wins,the probability of introducing a new product is $0.7$,and the corresponding probabilities for groups $B$ and $C$ are $0.6$ and $0.5$ respectively. The probability that the new product will be introduced is: