A number is chosen at random from the set $\{1,2,3, \ldots, 2000\}$. Let $p$ be the probability that the chosen number is a multiple of $3$ or a multiple of $7$ . Then the value of $500\ p$  is. . . . . . 

A coin is tossed $3$ times by $2$ persons. What is the probability that both get equal number of heads

What is the probability that when one die is thrown, the number appearing on top is even

A box contains $2$ black, $4$ white and $3$ red balls. One ball is drawn at random from the box and kept aside. From the remaining balls in the box, another ball is drawn at random and kept aside the first. This process is repeated till all the balls are drawn from the box. The probability that the balls drawn are in the sequence of $2$ black, $4$ white and $3$ red is

A coin is tossed until a head appears or until the coin has been tossed five times. If a head does not occur on the first two tosses, then the probability that the coin will be tossed $5$ times is

If $P(A) = 0.65,\,\,P(B) = 0.15,$ then $P(\bar A) + P(\bar B) = $