probability theory

1. We have a bag with 9 red marbles, 2 blue marbles and 3 green marbles in it. What is the probability of randomly selecting a nonblue marble from the bag?

2. If 8 red balls,7 blue balls 6 green balls. Find the probability of picking one ball that is red or green?

3. The probability of the students studying in Engineering is 40, and in medical is 50, and there are 20 students who study both, find the total number of students in the class?

4. The probability of students studying math is 30, of science is 40, and there are 12 students who study both, find the total number of student in the class?

5. In a class there are 50 students, twenty students like playing cricket and ten students like playing football. Find the probability of student who like both football and cricket?

6. Four persons are chosen from a group of 3 men, 2 women and 4 children. Find the probability of getting four persons, where exactly two persons are children?

7. Six cards are drawn at random from a pack of 52 cards. What is the probability that 3 cards are black and 3 cards are red?

8. A bag contains 3 red, 6 white and 7 blue balls. What is the probability that two balls drawn are red and white?

9. A card is drawn from a pack of 52 card, and drawn card is red card, now find the probability that the card drawn is greater than 7 and less than 11?

10. If probability of getting Wednesday and that a student is absent is 0.07 and there are 5 school days in a week, the probability that it is Wednesday is 0.7. Find that what is the probability that a student is absent given that day is Wednesday?

11. If P(B) = 2/3 and P(AB)= 2 / 7 then find P(A/B)?

12. If P (B) = 1/5 and P (AB) = 1 / 8 then find P (A/B)?

13. If P(Y) = 1/ 4 and P(XY)= 1 / 3 then find P(X/Y)?

14. Three people are to be seated on a bench. How many different sitting arrangements are possible if Erik must sit next to Joe?

15. How many 3-digit numbers satisfy the following conditions: The first digit is different from zero and the other digits are all different from each other?

16. Barbara has 8 shirts and 9 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants?

17. A credit card number has 5 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 6, the forth is divisible by 3 and the fifth digit is 3 times the sixth (which is any number bet 1-9). How many different credit card numbers exist?

18. In jar A there are 3 white balls and 2 green ones, in jar B there is one white ball and three green ones. A jar is randomly picked, what is the probability of picking up a white ball out of jar A?

19. When a card is drawn from a pack of 52 playing card, what is the probability of getting (a) an ace and a heart? (b) an ace or a heart?

20. Out of a box that contains 4 black and 6 white mice, three are randomly chosen. What is the probability that all three will be black?

21. There are 18 balls in a jar. You take out 3 blue balls without putting them back inside, and now the probability of pulling out a blue ball is 1/5. How many blue balls were there in the beginning?

22. In an Exam, the probability that students will pass and fail is 0.083. The probability that students will pass is 0.65. Then what is the probability that students will fail?

23. At a car park there are 100 vehicles, 60 of which are cars, 30 are vans and the remainder are lorries. If every vehicle is equally likely to leave, find the probability of:

a) van leaving first.

b) lorry leaving first.

c) car leaving second if either a lorry or van had left first.

24. When a fair dice is thrown, what is the probability of getting

a) the number 5

b) a number that is a multiple of 3

c) a number that is greater than 6

d) a number that is less than 7

25. Each of the letters HELLO is written on a card. A card is chosen at random from the bag. What is the probability of getting the letter ‘L’?

26. A bag contains 10 red marbles, 8 blue marbles and 2 yellow marbles. Find the experimental probability of getting a blue marble.

27. A bag contains 10 red marbles, 8 blue marbles and 2 yellow marbles. Find the theoretical probability of getting a blue marble.

28. Find the probability of rolling an even number when you roll a die containing the numbers 1-6. Express the probability as a fraction, decimal, ratio and percent.

29. The probability of getting a white ball from a bag of balls is . What is the probability of not getting a white ball?

30. A number is chosen at random from a set of whole numbers from 1 to 50. Calculate the probability that the chosen number is not a perfect square.

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