A bag contains $5$ white and $3$ black balls. Four balls are successively drawn out without replacement. What is the probability that they are alternately of different colours? What would be the probability of this event if balls are drawn with replacement?

A bag contains one black and two white balls. A drawing from the bag consists of taking a ball from the bag and keeping it out if it is white but putting it back if it is black. Calculate the probability that the first drawing is a white ball

A bag contains one black and two white balls. A drawing from the bag consists of taking a ball from the bag and keeping it out if it is white but putting it back if it is black. Calculate the probabilities that the second drawing is a white ball.

A bag contains one black and two white balls. A drawing from the bag consists of taking a ball from the bag and keeping it out if it is white but putting it back if it is black. Calculate the probability that the third drawing is a white ball.

A bag contains $4$ white and $2$ black balls. Another contains $3$ white and $5$ black balls. If one ball is drawn from each bag, then find the probability that both are white.

A bag contains $4$ white and $2$ black balls. Another contains $3$ white and $5$ black balls. If one ball is drawn from each bag, then find the probability that both are black.

A bag contains $4$ white and $2$ black balls. Another contains $3$ white and $5$ black balls. If one ball is drawn from each bag, then find the probability that one is white and one is black.

A bag contains $2$ black, $4$ white and $3$ red balls. One ball is drawn at random and kept aside. Then another ball is drawn and kept aside. This process is continued till all the balls are drawn. Find the probability that the ball drawn are in the sequence $2$ black, $4$ white and $3$ red.

A policeman fires four bullets on a dacoit. The probability that the dacoit will be killed by one bullet is $0.6$. What is the probability that the dacoit is still alive?