$A$ man draws a card from a pack of $52$ playing cards,replaces it,and shuffles the pack. He continues this process until he gets a card of spade. The probability that he will fail the first two times is

Two dice are thrown. The probability that the sum of the points on two dice will be $7$ is:

$A$ and $B$ are two independent events such that $P(A) = 1/2$ and $P(B) = 1/3$. Then $P$ (neither $A$ nor $B$) is equal to

$A$ bag contains $13$ red,$14$ green,and $15$ black balls. The probability of getting exactly $2$ black balls when pulling out $4$ balls is ${P_1}$. Now,the number of balls of each color is doubled,and $8$ balls are pulled out. The probability of getting exactly $4$ black balls is ${P_2}$. Then:

$A$ box contains $10$ good articles and $6$ with defects. One article is chosen at random. What is the probability that it is either good or has a defect?

$2$ persons $A$ and $B$ throw a die alternately until $1$ of them gets a '$6$' and wins the game. Find the probability of $B$ winning.