### Probability

1. In a box there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

2. A bag contains 5 green and 7 red balls. Two balls are drawn. The probability that one is green and the other is red is

3. A bag contains 5 white and 7 black balls and a man draws 4 balls at random. The odds against these being all black is :

4. Four balls are drawn at random from a bag containing 5 white, 4 green and 3 black balls. The probability that exactly two of them are white is :

5. The probability that when 12 balls are distributed among three boxes, the first will contain three balls is,

6. A bag contains 2 red, 3 green and 2 blue balls. 2 balls are to be drawn randomly. What is probability that the balls drawn contain no blue ball?

7. A bag has 13 red, 14 green and 15 white balls, p₁ is the probability of drawing exactly 2 white balls when four balls are drawn. Then the number of balls of each colour are doubled. Let p₂ be the probability of drawing 4 white balls when 8 ball are drawn, then

8. In a box carrying one dozen of oranges, one-third have become bad. If 3 oranges are taken out from the box at random, what is the probability that at least one orange out of the three oranges picked up is good?

9. A box contains 5 green, 4 yellow and 3 white marbles, 3 marbles are drawn at random. What is the probability that they are not of the same colour?

10. Two dice are thrown simultaneously. The probability of obtaining a total score of seven is

11. In each of a set of games it is 2 to 1 in favour of the winner of the previous game. The chance that the player who wins the first game shall win three at least of the next four is

12. A man and his wife appear for an interview for two posts. The probability of the husband’s selection is ¹⁄₇ and that of the wife’s selection is ⅕. The probability that only one of them will be selected is

13. In a single throw with four dice, the probability of throwing seven is:

14. Six dice are thrown. The probability that different number will turn up is :

15. There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, in a random order till both the faulty machines are identified. Then the probability that only two tests are needed is

16. The probability that a person will hit a target in shooting practice is 0.3. If he shoots 10 times, the probability that he hits the target is

17. The probability that A can solve a problem is ⅔ and B can solve it is ¾. If both attempt the problem, what is the probability that the problem gets solved?

18. Seven people seat themselves indiscriminately at round table. The probability that two distinguished persons will be next to each other is

19. The probability that two integers chosen at random and their product will have the same last digit is :

20. The probability that the birth days of six different persons will fall in exactly two calendar months is