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Topic 9: Statistics and Probability 1. In how many different ways can a ten – question true – false examination be answered? A 12 C 20 B 10 D 210 2. In how many can seven trees be planted in a circle? A 720 C 1440 B 5040 D 49 3. What is the number of permutation of the letters in the word “BANANA”? A 36 C 52 B 60 D 42 4. In a mathematics examination, a student may select 15 problems from a set of 20 problems. In how many can he make his choice? A 3,000 C 1,860,480 B 15,504 D 2,027 5. There are 10 basketball team registered every team twice, how many games are A 45 B 90

in the IECEP nationals. If each team plays played? C 180 D 120

6. How many three – digit numbers greater than 300 can be formed with the digits 1, 2, 3, 4 and 5 if no repetitions are allowed? A 3,125 C 120 B 1,875 D 36 7. In how many different ways can 5 persons be seated in an automobile having places for 2 in front seat and 3 in the back seat if only 3 can drive? A 30 C 36 B 60 D 72 8. How many ways can 4 boys and 4 girls be seated alternatively in the row of eight chairs? A 40,320 C 48 B 24 D 1,152 9. In how many different ways can 4 persons be seated in consecutive seats in a row of 7 seats? A 72 C 120 B 96 D 168 10. How many different committees of 6 can be formed from 12 boys and 20 girls if each committee is consisting of 4 boys and 2 girls? A 34,560 C 94,050 B 69,120 D 4,514,450 11. A team of 5 students is to be chosen for a math contest. If there were ten male and eight female students to chose from, what is the probability that the three team members will be male and two will be female? A 5/18 C 5/9 B 20/51 D None of these 12. How many different signals each consisting of 6 flags hung in a vertical can be formed from 4 identical red flag and 2 identical yellow flag? A 720 C 15 B 24 D 12

probability / page 2

13. How many 4 – digit numbers can be formed from the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, if repetition is allowed? A 4,536 C 5,040 B 10,000 D 9,000 14. Which of the following is not a probability value? A 0.992 C 8/10 B 13/12 D 0.01 15. If A and B are complimentary events and probability of occurrence of event A is zero, then P(B) is A Less than one C One B More than one D Zero 16. Determine the probability of throwing a total of 7 in a single throw with two dice. A 1/3 C 1/6 B 1/4 D 1/12 17. In one of the parlor games, 19 tickets from 1 to 19 are in the box. If two tickets are drawn at random. Determine the probability that both are odd. A 4/19 C 6/19 B 5/19 D 7/19 18. A box contains 4 red, 7 white and 5 blue balls. Two balls are chosen at random with replacement. What is the probability that they are both red? A 1/16 C 1/12 B 1/10 D 1/8 19. What is the probability of drawing either an ace or a king in a single draw from a deck of 52 playing cards? A 1/13 C 7/52 B 2/13 D 1/6 20. What is the probability of drawing either an ace or a heart in a single draw from a deck of 52 playing cards? A 17/52 C 9/26 B 4/13 D 15/52 21. From a bag containing 4 black balls and 5 white balls, two balls are drawn. Find the probability that one is black and the other is white. A 4/9 C 2/3 B 5/9 D 1/3 22. Two cards are drawn at random on an ordinary deck of cards. What is the probability that both cards are either a king or a diamond? A 16/169 C 4/13 B 20/221 D 17/52 23. Two red books and 4 blue books are placed at random on a shelf. What is the probability that the blue books will be together? A 0.1 C 0.2 B 0.143 D 0.025 24. A number 1 to 10,000 inclusive is selected at random. What is the probability that it is a perfect square? A 0.01 C 0.02 B 0.015 D 0.025

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25. What is the probability of drawing 3 face cards in 3 draws from an ordinary deck of cards?

A 0.0123 B 0.00995

C 0.123 D 0.0995

26. If 10 coins are tossed, what is the probability that it will show 5 heads and 5 tails? A 0.246 C 0.0246 B 0.256 D 0.0256 27. What is the probability of getting a number “4” thrice in five tosses of a dice? A 0.232 C 0.0232 B 0.322 D 0.0322 28. There is 1 defective per 100 items of a product in a long run. What is the probability that there is one and only one defective in a random lot of 100? A 0.3697 C 0.3796 B 0.3967 D 0.3679 29. In how many can the IECEP chapter with 15 directors choose a president, a vice president, a secretary, a treasurer and an auditor, if no member can hold more than one position? A 630,630 C 360,360 B 3,300 D 3003 30. A two – digit number is chosen randomly. What is the probability that it is divisible by 7? A 7/50 C 1/7 B 13/90 D 5/7

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in the IECEP nationals. If each team plays played? C 180 D 120

6. How many three – digit numbers greater than 300 can be formed with the digits 1, 2, 3, 4 and 5 if no repetitions are allowed? A 3,125 C 120 B 1,875 D 36 7. In how many different ways can 5 persons be seated in an automobile having places for 2 in front seat and 3 in the back seat if only 3 can drive? A 30 C 36 B 60 D 72 8. How many ways can 4 boys and 4 girls be seated alternatively in the row of eight chairs? A 40,320 C 48 B 24 D 1,152 9. In how many different ways can 4 persons be seated in consecutive seats in a row of 7 seats? A 72 C 120 B 96 D 168 10. How many different committees of 6 can be formed from 12 boys and 20 girls if each committee is consisting of 4 boys and 2 girls? A 34,560 C 94,050 B 69,120 D 4,514,450 11. A team of 5 students is to be chosen for a math contest. If there were ten male and eight female students to chose from, what is the probability that the three team members will be male and two will be female? A 5/18 C 5/9 B 20/51 D None of these 12. How many different signals each consisting of 6 flags hung in a vertical can be formed from 4 identical red flag and 2 identical yellow flag? A 720 C 15 B 24 D 12

probability / page 2

13. How many 4 – digit numbers can be formed from the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, if repetition is allowed? A 4,536 C 5,040 B 10,000 D 9,000 14. Which of the following is not a probability value? A 0.992 C 8/10 B 13/12 D 0.01 15. If A and B are complimentary events and probability of occurrence of event A is zero, then P(B) is A Less than one C One B More than one D Zero 16. Determine the probability of throwing a total of 7 in a single throw with two dice. A 1/3 C 1/6 B 1/4 D 1/12 17. In one of the parlor games, 19 tickets from 1 to 19 are in the box. If two tickets are drawn at random. Determine the probability that both are odd. A 4/19 C 6/19 B 5/19 D 7/19 18. A box contains 4 red, 7 white and 5 blue balls. Two balls are chosen at random with replacement. What is the probability that they are both red? A 1/16 C 1/12 B 1/10 D 1/8 19. What is the probability of drawing either an ace or a king in a single draw from a deck of 52 playing cards? A 1/13 C 7/52 B 2/13 D 1/6 20. What is the probability of drawing either an ace or a heart in a single draw from a deck of 52 playing cards? A 17/52 C 9/26 B 4/13 D 15/52 21. From a bag containing 4 black balls and 5 white balls, two balls are drawn. Find the probability that one is black and the other is white. A 4/9 C 2/3 B 5/9 D 1/3 22. Two cards are drawn at random on an ordinary deck of cards. What is the probability that both cards are either a king or a diamond? A 16/169 C 4/13 B 20/221 D 17/52 23. Two red books and 4 blue books are placed at random on a shelf. What is the probability that the blue books will be together? A 0.1 C 0.2 B 0.143 D 0.025 24. A number 1 to 10,000 inclusive is selected at random. What is the probability that it is a perfect square? A 0.01 C 0.02 B 0.015 D 0.025

probability / page 3

25. What is the probability of drawing 3 face cards in 3 draws from an ordinary deck of cards?

A 0.0123 B 0.00995

C 0.123 D 0.0995

26. If 10 coins are tossed, what is the probability that it will show 5 heads and 5 tails? A 0.246 C 0.0246 B 0.256 D 0.0256 27. What is the probability of getting a number “4” thrice in five tosses of a dice? A 0.232 C 0.0232 B 0.322 D 0.0322 28. There is 1 defective per 100 items of a product in a long run. What is the probability that there is one and only one defective in a random lot of 100? A 0.3697 C 0.3796 B 0.3967 D 0.3679 29. In how many can the IECEP chapter with 15 directors choose a president, a vice president, a secretary, a treasurer and an auditor, if no member can hold more than one position? A 630,630 C 360,360 B 3,300 D 3003 30. A two – digit number is chosen randomly. What is the probability that it is divisible by 7? A 7/50 C 1/7 B 13/90 D 5/7

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