Directions (for Q. Nos. 1 to 3) A bag contains 8 red and 4 green balls. Find the probability that

1. All the 4 balls drawn are green when four bells are drawn at random.

Directions (for Q. Nos. 1 to 3) A bag contains 8 red and 4 green balls. Find the probability that

2. Two balls are red and one ball is green when three balls are drawn at random.

Directions (for Q. Nos. 1 to 3) A bag contains 8 red and 4 green balls. Find the probability that

3. Three balls are drawn and none of them is red.

4. The odds in favour of an event are 2:7. Find the probability of occurrence of this event.

5. The odds against of an event are 5:7, find the probability of occurrence of this event.

6. If there are two children in a family, find the probability that there is atleast one girl in the family.

7. From a group of 3 men and 2 women, two persons are selected at random. Find the probability that atleast one woman is selected.

8. A box contains 5 defective and 15 non-defective bulbs. Two bulbs are chosen at random. Find the probability that both the bulbs are non-defective.

9. In the previous question (number 58), find the probability that atleast 3 bulbs are defective when 4 bulbs are selected at random.

10. If A and B be two events in a sample space such that P(A) = 3/10 and P(B) = 1/2  and P(A∩B)= 1/5. Find P(A∪B).

11. If A and B be two events in a sample space such that P(A) =2/5 ,P(B)=1/2 and P(AUB) = 3/5, find P(A∩B)

12. If P (A¯) = 0.65, P(AUB) = 0.65, where A and B are two mutually exclusive events, then find P(B).

13. If A,B and C are three mutually exclusive and exhaustive events. Find P(A), if P(B)= 3/2P(A) and P(C) =1/2 P(B).

14. Two dice are tossed once. Find the probability of getting an even number on first die, or a total of 8.

15. A die is thrown twice, what is the probability that atleast one of the two throws comes up with the number 5?

16.In a single throw of two dice, find the probability that neither a doublet nor a total of 8 will appear.

17. A die is thrown twice, what is the probability that atleast one of the two numbers is 6?

18. A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of its being a heart or a king.

19. Two cards are drawn at random from a well-shuffled pack of 52 cards. What is the probability that either both are red or both are queens?

20. A card is drawn from a deck of 52 cards. Find the probability of getting a red card or a heart or a king.

21. Four cards are drawn at a time from a pack of 52 playing cards. Find the probability of getting all the four cards of the same suit.

22.From a well-shuffled pack of 52 cards, a card is drawn at random. Find the probability that the drawn card is a king or a queen.

23. Two cards are drawn at random from a pack of 52 cards. What is the probability that either both are black or both are jacks?

24. A natural number is chosen at random from amongst the first 300. What is the probability that the number, so chosen is divisible by 3 or 5?

25. A natural number is chosen at random from the first 100 natural numbers. What is the probability that the number chosen is a multiple of 2 or 3 or 5?

26. A box contains 5 red balls, 8 green balls and 10 pink balls. A ball is drawn at random from the box. What is the probability that the ball drawn is either red or green?

27. A basket contains 10 apples and 20 oranges out of which 3 apples and 5 oranges are defective. If we choose two fruits at random, what is the probability that either both are oranges or both are non defective?

28. In a class 40% of the students offered Physics 20% offered Chemistry and 5% offered both. If a student is selected at random, find the probability that he has offered Physics or Chemistry only.

29. The probability that an MBA aspirant will join IIM is 2/5 and that he will join XLRI is 1/3. Find the probability that he will join IIM or XLRI.

30. In a given race, the odds in favour of horses H_1, H_2, H_3 and H₄ are 1:2, 1:3, 1:4,1:5 respectively. Find the probability that one of them wins the race.