Two dice are thrown simultaneously. What is the probability of obtaining a multiple of $2$ on one of them and a multiple of $3$ on the other

An experiment consists of rolling a die and then tossing a coin if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.

Three coins are tossed once. Find the probability of getting no head.

In each of the following experiments specify appropriate sample space A person is noting down the number of accidents along a busy highway during a year.

Cards are drawn one by one without replacement from a pack of $52$ cards. The probability that $10$ cards will precede the first ace 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