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Math Exercises: Probability

 

 

 

 

1. What is the probability of throwing one dice and getting the number greater than 4 ?

 

2. What is the probability of throwing two dice and getting the sum of the fallen numbers greater than 3 ?

 

3. We select 7 playing cards out of 32. What is the probability that among the selected cards there are exactly three hearts ?

 

4. What is the probability of flipping a coin and getting the head fallen five times in a row ?

 

5. The customer wants to buy a bread and a can. There are 30 pieces of bread in the shop, including 5 from the previous day, and 20 cans with unreadable expiration date, of which one has expired. What is the probability that the customer will buy a fresh bread and a tin under warranty ?

 

6. Abstracted secretary placed three letters randomly into three envelopes. What is the probability that at least one of the recipients gets his letter ?

 

7. There are 10 pots exposed in the shop, 2 of which have hidden defects. The customer buys two pieces. What is the probability that at least one of them has a hidden bug ?

 

8. What is the probability of throwing one dice seven times in a row and getting the number 6 fallen exactly 3 times ?

 

9. The test contains 10 questions, each one with available four different answers, among which just one is correct. To pass the test at least 5 questions must be answered correctly. What is the probability that completely unprepared student will pass the test ?

 

10. We have 100 tickets in the hat numbered from 1 to 100. With what probability will we pull out a number that is divisible by two or by five ?

 

11. There are 49 products in the box, from which only 6 are high quality. What is the probability of pulling out 6 random products from the box and having at least four of them high quality ?

 

12. What is the probability of throwing two dice and getting the sum of the fallen numbers exactly 9 ?

 

13. What is the probability of throwing one dice and get :
a) the even number
b) the number divisible by three
c) the number less than six ?

 

14. There are 60 chemical flasks in the laboratory, 6 of which are incorrectly labeled. What is the chance that if we randomly choose 5 flasks, exactly 3 of them will be labeled correctly ?

 

15. What is the probability that if we choose a trinity from 19 boys and 12 girls, we will have :
a) three boys
b) three girls
c) two boys and one girl ?

 

16. There are 30 products in the box, from which 3 are faulty. Find the probability of pulling out 5 random products from the box and having among them at most two the faulty ones.

 

17. Johnny wrote a random natural number from 1 to 20. Determine the probability that he wrote a prime number.

 

18. Suzie has available the digits 0, 2, 3, 4, 5, 6, 7. What is the probability that when she creates a random three-digit number from the given digits, it will be the number 445 ?

 

19. Out of 100 pairs of shoes 5 pairs are of poor quality. The auditor selects randomly four pairs of the shoes. What is the probability that at least one from the selected pairs is of poor quality ?

 

20. In the lottery 5 numbers are drawn from among 35. For 3 correctly guessed numbers lottery pays the third prize. What is the probability of winning the third prize, if we submit just one ticket with 5 guessed numbers ?

 

21. In the mall they have 100 TV sets, of which 85 are of the first and 15 are of the second quality. The first ten customers received the TV set of the first quality. What is the probability that the eleventh customer will buy the TV set of the second quality ?

 

22. We have 4 white and 3 blue balls in a bowl. Accidentally we pull out two balls. What is the probability that :
a) both of the pulled out balls are white
b) one ball is white and the other one is blue ?

 

23. What is the probability of throwing three dice and
a) get the sum of the fallen numbers exactly 9 ?
b) get the sum of the fallen numbers exactly 10 ?
c) Explain why when throwing three dice the sum of 10 falls more often than the sum of 9.

 

24. There are 800 components in the warehouse, 20 of which are broken. What is the probability that between 9 randomly selected components no more than 3 of them will be broken ?

 

25. In the class of 30 students, seven of them don't have done the homework. The teacher choosed randomly 6 students. What is the chance that at least four of them have done their homework ?

 

26. Four gentlemen have put off four identical hats in the locker room. What is the probability that on leaving at least one of them will get back his own hat ?

 

27. What is the probability of throwing one dice three times in a row and get the even number after the first fall, the number greater than four after the second fall and the odd number after the last fall ?

 

28. Three shooters shoot at the same target, each of them shoots just once. The first one hits the target with a probability of 70%, the second one with a probability of 80% and the third one with a probability of 90%. What is the probability that the shooters will hit the target
a) at least once
b) at least twice ?

 

29. The probability that the bulb will work longer than 800 hours is 0.2. We have three bulbs in the hallway. What is the probability that after 800 hours of service at least one of them will still work ?

 

30. In the lottery 6 numbers are drawn out of 49. What is the probability of winning
a) the second prize (we guessed 5 numbers correctly)
b) the third prize (we guessed 4 numbers correctly)
if we were guessing just six numbers ?

 

 

 

 

 

 

You might be also interested in:

- Mathematical Statistics

- Variations, Permutations, Combinations

- Factorials and Combinatorial Expressions

- Combinatorial Equations and Inequalities

 

 
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