The probability of happening an event $A$ is $0.5$ and that of $B$ is $0.3$. If $A$ and $B$ are mutually exclusive events, then the probability of happening neither $A$ nor $B$ is

In a game, a man wins $Rs.\,100$  if he gets $5$ or $6$ on a throw of a fair die and loses $Rs.\,50$ for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is

A box containing $4$ white pens and $2$ black pens. Another box containing $3$ white pens and $5$ black pens. If one pen is selected from each box, then the probability that both the pens are white is equal to

A bag contains $4$ white, $5$ black and $6$ red balls. If a ball is drawn at random, then what is the probability that the drawn ball is either white or red

The probabilities of a problem being solved by two students are $\frac{1}{2},\frac{1}{3}$. Then the probability of the problem being solved is

Two dices are rolled. If both dices have six faces numbered $1,2,3,5,7$ and $11,$ then the probability that the sum of the numbers on the top faces is less than or equal to $8$ is