Monday, January 25, 2016 Practice Quiz Counting Probability

Wednesday, May 3, 2023

Practice QuizCounting

Probability

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 73

Students studying languages = 12 + 7 + 3 = 22

Students studying neither = 30 – 22 = 8

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?

PossibleOutfits = Shirts Pants Shoes

40 = 5 Pants 2

40 = 10 Pants4 = Pants

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 = Males Females+

Males = 2xFemales = x

24 = 2x x+24 = 3x8 = x

82(8) = 16

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 = 16Females = 8

Males with D.L. = ¼ 16Males with D.L. = 4

Females D.L. = Males D.L.–Students D.L.Females D.L. = 4–12Females D.L. = 8

FemalesWithoutD.L. = 0

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 = 26Football = 27Baseball = 24

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 + 622 = x + 2 + 9 + 622 = x + 175 = x Smithsonian = 5 + 2 + 3 + 10

Smithsonian = 20

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?

___ ___ ___ ___ ___

1st

Letter1st

digit2nd

digit3rd

digit

26Number of choices

10 10 10

= 676,000

Answer: 676,000 possible combinations

2nd Letter

26

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)2550

1550+ = 40

50= 4

5

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)

720

520+ = 12

20= 3

5

redred

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)# girls

# girls + #boys 12

12 14

1226

6 13

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

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 3rd red)

# red# red + #black

1010 12

1022

5 11

10 red checkers + 12 black checkers = 22 checkers

10

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

sectors with #2total number of sectors

2 6

1 3

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

sectors with prime numbertotal number of sectors

5 6

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

number of yellowtotal number of jellybeans

14

14

6 1 14 6 4x

6 1 20 4x

(1)(x + 20) = (6)(4)

x + 20 = 24–20 –20

x = 4

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)

14

P(#5 on 1st roll) AND P(#5 on 2nd roll)16

16 = 1

36

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(1st blueberry AND 2nd blueberry)

15

P(1st blueberry) AND P(2nd bluberry)

26

15 = 2

30

Eating each muffin involves removing an itemwithout replacement.

= 115

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 = s2

A = 62

A = 36

A = r2A = 32

d = 6

A = 9A = 9

P(circle)square of areacircle of area

Circle area Square area

P(circle)369

4

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 = 32A = 9 = 9

P(shaded) Big area Small areaBig area

A = r2Big area

P(shaded)9 4

9

59

A = 22A = 4 = 4

A = r2Small area

5 9

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 = s2 = 32 = 9

1Ratio

area of shadedarea of ABCD

Big Square Area

2

1

2

Triangle Area 1

2A bh

b=

h=11

22 = 1

Area of 4 triangles1= 4(1) = 4

1 1

1

18


1Big Square Area = 9

2

1

2

Area of 4 triangles

1

= 41 1

1Big Square

Area4 Triangle

Area–=Area of Square ABCD

= 9 – 4 = 5

(shaded area)

18


1

Ratioarea of shadedarea of ABCD

2

1

2

b=

h=1

1 1

1

Area of 4 triangles = 4(shaded area)

Area of Square ABCD = 5

4Ratio5

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.

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?

___ ___ ___ ___

1st

letter2nd

letter3rd

letter4th

letter

4Number of choices

5 5 5 = 500

Answer: 500 arrangements

21

Find the number of ways you can arrange

all the letters in the word MATH.

___ ___ ___ ___

1st

letter2nd

letter3rd

letter4th

letter

4Number of choices

3 2 1 = 24


22

Find the number of ways you can arrange

two letters in the word MATH.

___ ___

1st

letter2nd

letter

4Number of choices

3 = 12


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

23a

How many people ordered cakes?

Cake Pie

4

Cookies

3

5

1

6 2

0

6 + 2 + 3 + 0 = 11

23b

How many people ordered

pies and cookies?

Cake Pie

4

Cookies

3

5

1

6 2

0

3 + 1 = 4

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

23d

How many people orderedcakes and pies and cookies?

Cake Pie

4

Cookies

3

5

1

6 2

0

3

23e

How many people orderedcookies and no cake?

Cake Pie

4

Cookies

3

5

1

6 2

0

4 + 1 = 5

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?

146

P(green AND red)

P(green) P(red)AND

138

73

138

=9124

AND

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?

94

P(1st black AND 2nd black)P(1st black) P(2nd black)AND

83

13

12 =

61

Each cat leaves the cage without replacement.

48

12

39

13

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Monday, January 25, 2016 Practice Quiz Counting Probability