Two fair dice are tossed. Let $A$ be the event that the first die shows an even number and $B$ be the event that the second die shows an odd number. The two event $A$ and $B$ are

Two dice are thrown together. If the numbers appearing on the two dice are different, then what is the probability that the sum is $6$

One card is drawn from a well shuffled deck of $52$ cards. If each outcome is equally likely, calculate the probability that the card will be a diamond not an ace

In a class of $60$ students, $40$ opted for $NCC,\,30$ opted for $NSS$ and $20$ opted for both $NCC$ and $NSS.$ If one of these students is selected at random, then the probability that the student selected has opted neither for $NCC$ nor for $NSS$ is

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

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