$3$ coins are tossed. Find the probability of getting all heads.

$A$ bag $A$ contains $2$ white and $3$ red balls and bag $B$ contains $4$ white and $5$ red balls. One ball is drawn at random from a randomly chosen bag and is found to be red. The probability that it was drawn from bag $B$ is:

Among $15$ players,$8$ are batsmen and $7$ are bowlers. Find the probability that a team is chosen of $6$ batsmen and $5$ bowlers.

$A$ 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?

Two numbers are selected at random from $1, 2, 3, \dots, 100$ and are multiplied. The probability, correct to two decimal places, that the product thus obtained is divisible by $3$ is:

$A$ jar contains $3$ red marbles,$7$ green marbles and $10$ white marbles. If a marble is drawn from the jar at random,what is the probability that this marble is white?