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Practice Quiz Counting Probability

This practice quiz tests your knowledge of counting probability. Answer questions about students studying languages, doll's wardrobe outfits, class demographics, sports, and more.

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Practice Quiz Counting Probability

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  1. Practice QuizCountingProbability

  2. There are 30 students in Mary’s homeroom. Of these students, 15 are studying Spanish, 10 are studying Latin, and 3 are studying both languages. How many students are studying neither language? 1 Spanish Latin 12 7 3 Students studying languages = 12 + 7 + 3 = 22 Students studying neither = 30 – 22 = 8

  3. A doll’s wardrobe consists of 40 possible outfits consisting of a shirt, pants, and a pair of shoes. If there are 5 shirts and 2 pairs of shoes, how many pairs of pants are in the doll’s wardrobe? 2 Possible Outfits   = Shirts Pants Shoes   = 40 5 Pants 2  = 40 10 Pants = 4 Pants

  4. In a class of 24 students, there are twice as many male students as female students. Twelve students have a driver’s license. One quarter of the male students have a driver’s license. How many females in the class do not have a driver’s license? 3 Females = x 8 Males = 2x 2(8) = 16 + = Students Males Females + = 24 2x x = 24 3x = 8 x

  5. In a class of 24 students, there are twice as many male students as female students. Twelve students have a driver’s license. One quarter of the male students have a driver’s license. How many females in the class do not have a driver’s license? 3 Females = 8 ¼ Males = 16  = Males with D.L. Males Females Without D.L. = 0 ¼  = Males with D.L. 16 = Males with D.L. 4 – = Males D.L. Females D.L. Students D.L. – = 4 Females D.L. 12 = Females D.L. 8

  6. The diagram shows the results of a survey asking which sport members of the Key Club watch on television. Which of the following statements are true? 4 Tennis = 26 Football = 27 Baseball = 24

  7. The diagram shows the Washington, D.C. attractions visited by a social studies class. If 22 students visited the Capitol, how many students visited the Smithsonian? 5 Capitol = x + 2 + 9 + 6 22 = x + 2 + 9 + 6 22 = x + 17 Smithsonian = 5 + 2 + 3 + 10 5 = x Smithsonian = 20

  8. The combination for your school locker consists of two letters followed by three digits. How many combinations are possible if all letters and digits can be used more than once? 6 1st Letter 2nd Letter 1st digit 2nd digit 3rd digit     ___ ___ ___ ___ ___ 26 26 10 10 10 Number of choices = 676,000 Answer: 676,000 possible combinations

  9. A box contains 50 marbles. Twenty-five are red, 15 are white, and 10 are blue. Steve took a marble without looking. What is the probability that the marble is not blue? 7 P(not blue) P(red OR white) P(red) OR P(white) + = =

  10. A bag contains 3 round blue pegs, 2 round red pegs, 5 square red pegs, 4 square yellow pegs, and 6 square blue pegs. One peg dropped out of the bag. What is the probability that it was red or round? red 8 red P(red OR round) P(red) OR P(round) + = =

  11. A class roster lists 15 boys and 12 girls. Two students are randomly selected to speak at a school assembly. If one of the students selected is a boy, what is the probability that the other student selected is a girl? 9 There are 15 boys. One boy is selected. There are now 14 boys. P(selecting girl)

  12. A bag contains an equal number of red and black checkers. Altogether, there are 24 checkers in the bag. A red checker is drawn from the bag and not replaced. A second red checker is drawn from the bag and not replaced. What is the probability that a third checker drawn from the bag will be red? 10 12 red checkers / 12 black checkers 11 red checkers / 12 black checkers Draw 1 red 10 red checkers / 12 black checkers Draw 1 red Total checkers = 10 + 12 = 22

  13. A bag contains an equal number of red and black checkers. Altogether, there are 24 checkers in the bag. A red checker is drawn from the bag and not replaced. A second red checker is drawn from the bag and not replaced. What is the probability that a third checker drawn from the bag will be red? 10 10 red checkers + 12 black checkers = 22 checkers P(selecting 3rd red)

  14. Each sector in the spinner is of equal size and there is no overlap. The spinner is equally likely to stop on any sector. What is the probability that the spinner will land on sector 2? 11 P(landing on sector 2)

  15. Each sector in the spinner is of equal size and there is no overlap. The spinner is equally likely to stop on any sector. What is the probability that the spinner will land on a sector labeled with a prime number? 12 P(landing on prime number)

  16. A box contains colored jellybeans. There are 14 red, 6 yellow, and x blue jellybeans in the bag. If the probability of drawing a yellow jellybean is , what is the value of x? 13 P(yellow) x + 20 = 24 –20 –20 x = 4 (1)(x + 20) = (6)(4)

  17. 14 If a die is rolled twice, what is the probability that is lands on 5 both times? P(#5 on 1st roll AND #5 on 2nd roll) P(#5 on 1st roll) AND P(#5 on 2nd roll)  =

  18. A box contains 6 muffins, only two of which are blueberry muffins. If Carol randomly selects a muffin from the box and eats it and then Kerry also randomly takes a muffin from the box and eats it, what is the probability that both muffins are blueberry? 15 Eating each muffin involves removing an item without replacement. P(1st blueberry AND 2nd blueberry) P(1st blueberry) AND P(2nd bluberry)  = =

  19. 16 A circular target is inscribed in a square base. The radius of the circle is 3. Assuming that a dart randomly strikes the figure, what is the probability that it lands in the circle? P(circle) d = 6 Circle area Square area A = r2 A = s2 A = 32 A = 62 6 A = 9 A = 36 A = 9 P(circle)

  20. 17 A target is made up of concentric circles as shown in the figure. Assuming that a dart randomly strikes the target, what is the probability that it will strike the shaded region? P(shaded) Big area Small area A = r2 A = r2 A = 32 A = 22 A = 9 = 9 A = 4 = 4 P(shaded)

  21. 18 2 In the figure above, ABCD and WXYZ are squares. If AX = 1 and XB = 2, what is the ratio of the area of the shaded regions to the area of ABCD? 1 1 Ratio 1 Triangle Area = 1 2 h= 1 = 4(1) = 4 1 Area of 4 triangles b= 1 Big Square Area A = s2 = 32 = 9

  22. 18 = 4 2 Area of 4 triangles In the figure above, ABCD and WXYZ are squares. If AX = 1 and XB = 2, what is the ratio of the area of the shaded regions to the area of ABCD? (shaded area) 1 1 1 Big Square Area = 9 Area of Square ABCD 4 Triangle Big Square 2 – = 1 Area Area 1 = 9 – 4 1 = 5

  23. 18 = 4 Area of 4 triangles 2 In the figure above, ABCD and WXYZ are squares. If AX = 1 and XB = 2, what is the ratio of the area of the shaded regions to the area of ABCD? (shaded area) 1 1 Ratio 1 Area of Square ABCD = 5 2 h= 1 1 b= 1

  24. The table shows the items that can be selected for a pizza order. How many pizza combinations can you order with 1 meat, 1 vegetable, and 1 cheese? 19 There are 3 • 2 •3 = 18 pizza combinations.

  25. How many possible 4-letter arrangements of the letters in the word EGYPT are there, if E cannot be the first letter and the letters can be repeated? 20 1st letter 2nd letter 3rd letter 4th letter    = ___ ___ ___ ___ 4 5 5 5 500 Number of choices Answer: 500 arrangements

  26. Find the number of ways you can arrange all the letters in the word MATH. 21 1st letter 2nd letter 3rd letter 4th letter    = ___ ___ ___ ___ 4 3 2 1 24 Number of choices Answer: 24 arrangements

  27. Find the number of ways you can arrange two letters in the word MATH. 22 1st letter 2nd letter  = ___ ___ 12 4 3 Number of choices Answer: 12 arrangements

  28. 23 Cake Pie 6 5 2 3 The Venn Diagram illustrates a relationship between cake, cookie, and pie orders at a bakery. 0 1 4 Cookies

  29. 23a Cake Pie 6 5 2 3 How many people ordered cakes? 0 1 4 Cookies 6 + 2 + 3 + 0 = 11

  30. 23b Cake Pie 6 5 2 3 How many people orderedpies and cookies? 0 1 4 Cookies 3 + 1 = 4

  31. 23c Cake Pie 6 5 2 3 How many people ordered pies or cookies? 0 1 4 Cookies 5 + 2 + 3 + 1 + 0 + 4 = 15

  32. 23d Cake Pie 6 5 2 3 How many people orderedcakes and pies and cookies? 0 1 4 Cookies 3

  33. 23e Cake Pie 6 5 2 3 How many people orderedcookies and no cake? 0 1 4 Cookies 4 + 1 = 5

  34. Your drawer contains 8 red socks and six green socks. It is too dark to see which are which. What is the probability that you pick a green sock, then a red sock? 24 AND P(green AND red) AND P(green) P(red)  = 

  35. There are four black cats and five grey cats in a cage, and none of them want to be in there. The cage door opens briefly and two cats escape. What is the probability that both escaped cats are black? 25 Each cat leaves the cage without replacement. P(1st black AND 2nd black) P(2nd black) AND P(1st black)  = 

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