7th Grade Math

Selected Answers and Solutions R23

Selected Answers and Solutions

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9.

4

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  4 484
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11. Sample answer:

H

H T H T H T H T

H

T

T

H

T

Dime Nickel Sample

Space

Quarter

HHH

HHT

HTH

HTT

THH

THT

TTH

TTT

Elba wins

Elba wins

Elba wins

Steve wins

Elba wins

Steve wins

Steve wins

Steve wins

There are 8 equally likely outcomes with 4 favoring

Elba. So, the probability that Elba wins is _ 84 or _^12.

1313 a. One of eight outcomes has three boys.

Therefore, P(all three children will be boys) = _^18.

b. Six outcomes include at least one boy and one

girl. Therefore, P(at least one boy and one girl) = _^68

or _^34. c. Three outcomes have two boys and one

girl. Therefore, P(two boys and one girl) = _^38.

d. Four outcomes have at least two girls.

Therefore, P(at least two girls) = _^48 or _^12. e. There

is only 1 outcome in which the fi rst two born are

boys and the last born is a girl. Therefore, P(the fi rst

two born are boys and the last born is a girl) = _^18.

15a. 16 15b. _ 161

15c.

black

yellow

green

black, yellow

black, green

black black, black

white black, white

yellow

yellow

green

yellow, yellow

yellow, green

black yellow, black

white yellow, white

Sample

Shoes Socks Space

17. The fi rst outcome in the I bracket should be IC.


18. Sample game: Each player tosses a coin 10 times.
    If it comes up heads, player 1 receives 1 point. If it
    comes up tails, player 2 receives 1 point. The player
    with the most points at the end of 20 tosses wins.


19. 12 23. _ 112

Pages 441–443 Lesson 8-1C

11 There are two outcomes for tossing the quarter,

two for tossing the dime and two for tossing the

nickel. The Fundamental Counting Principle says

that you can multiply to fi nd out the total number

of outcomes: 2 · 2 · 2 = 8 outcomes.

3. 72; 72 _^1 or about 1.4%; unlikely 5. 140 7. 12


4. 16 11. 18 possible bread choices; _ 181 ; very unlikely
   1313 The total number of T-shirt choices is the
   product of the number of designs and the number
   of color choices, or 32 · 11 or 352 choices. The
   advertisement is not true because there are
   365 days in a year.


5. 2; 4; 8; 2n; Sample answer: I used a pattern to
   determine the number of outcomes for n coins. One
   coin: 2^1 outcomes, two coins: 2 · 2 or 2^2 outcomes,
   three coins: 2 · 2 · 2 or 2^3 outcomes, n coins: 2n
   outcomes. 17. Sample answer: Both are methods
   used to fi nd the total number of possible outcomes.
   The Fundamental Counting Principle is a
   computational procedure therefore is a much faster
   method of obtaining the total number of outcomes
   than drawing a tree diagram. Tree diagrams allow
   you to see the specifi c outcomes. The Fundamental
   Counting Principle only gives the number of
   outcomes. 19. 6 21. ^12 23. ^18

Pages 445–447 Lesson 8-1D

1. 5,040
   33 There are 5 choices for the fi rst DVD. There are
   4 choices that remain for the second DVD. Since
   5 · 4 = 20, there is a _ 201 chance of selecting Season
   1 followed by Season 2.

R01_R42_EM_SelAns_895130.indd R23 1/18/10 9:51 AM