1. Monday, January 25, 2016 Practice Quiz Counting Probability

2. 1 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? Spanish Latin 12 7 3 Students studying languages = 12 + 7 + 3 = 22 Students studying neither = 30 – 22 = 8

3. 2 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? Possible Outfits = ShirtsPantsShoes  40 = 5Pants2  40 = 10Pants  4 =

4. 3 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? Students = MalesFemales + Males = 2x Females = x 24 = 2xx + 24 = 3x 8 = x 8 2(8) = 16

5. 3 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? Males with D.L. = ¼ Males  Males = 16 Females = 8 Males with D.L. = ¼ 16  Males with D.L. = 4 Females D.L. = Males D.L. – Students D.L. Females D.L. = 4 – 12 Females D.L. = 8 Females Without D.L. = 0

6. 4 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? Tennis = 26 Football = 27 Baseball = 24

7. 5 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? Capitol = x + 2 + 9 + 6 22 = x + 2 + 9 + 6 22 = x + 17 5 = x Smithsonian = 5 + 2 + 3 + 10 Smithsonian = 20

8. 6 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? ___ ___ ___ ___ ___ 1 st Letter 1 st digit 2 nd digit 3 rd digit 26 Number of choices 10  = 676,000 Answer: 676,000 possible combinations 2 nd Letter 26 

9. 7 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? P(not blue) P(red OR white) P(red) OR P(white) + ==

10. 8 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? P(red OR round) P(red) OR P(round) + == red

11. 9 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? There are 15 boys. One boy is selected. There are now 14 boys. P(selecting girl)

12. 10 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? 12 red checkers / 12 black checkers Draw 1 red 11 red checkers / 12 black checkers Draw 1 red 10 red checkers / 12 black checkers 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? P(selecting 3 rd red) 10 red checkers + 12 black checkers = 22 checkers 10

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? P(landing on sector 2) 11

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? P(landing on prime number) 12

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? P(yellow) 13 (1)(x + 20) = (6)(4) x + 20 = 24 –20 x = 4

17. If a die is rolled twice, what is the probability that is lands on 5 both times? P(#5 on 1 st roll AND #5 on 2 nd roll) 14 P(#5 on 1 st roll) AND P(#5 on 2 nd 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? P(1 st blueberry AND 2 nd blueberry) 15 P(1 st blueberry) AND P(2 nd bluberry)  = Eating each muffin involves removing an item without replacement. =

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? 6 A = s 2 A = 6 2 A = 36 A =  r 2 A =  3 2 d = 6 A =  9 A = 9  P(circle) Circle area Square area 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? A =  3 2 A =  9= 9  P(shaded) A =  r 2 Big area P(shaded) A =  2 2 A =  4= 4  A =  r 2 Small area

21. 18 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? A = s 2 = 3 2 = 9 1 Ratio Big Square Area 2 1 2 Triangle Area b=b= h=h= = 1 Area of 4 triangles 1 = 4(1) = 4 11 1

22. 18 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 Big Square Area = 9 2 1 2 Area of 4 triangles 1 = 4 11 1 Big Square Area 4 Triangle Area – = Area of Square ABCD = 9 – 4 = 5 (shaded area)

23. 18 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 Ratio 2 1 2 b=b= h=h= 1 11 1 Area of 4 triangles = 4 (shaded area) Area of Square ABCD = 5

24. 19 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? There are 3 2 3 = 18 pizza combinations.

25. 20 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? ___ ___ 1 st letter 2 nd letter 3 rd letter 4 th letter 4 Number of choices 555  = 500 Answer: 500 arrangements

26. 21 Find the number of ways you can arrange all the letters in the word MATH. ___ ___ 1 st letter 2 nd letter 3 rd letter 4 th letter 4 Number of choices 321  = 24 Answer: 24 arrangements

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

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

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

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

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

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

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

34. 24 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? P(green AND red) P(green)P(red) AND   =

35. 25 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? P(1 st black AND 2 nd black) P(1 st black) P(2 nd black) AND   = Each cat leaves the cage without replacement.