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Probability | Grade 7

Student Concept Worksheet Answers
1
a) 8 outcomes | b) 4/8 = 1/2 | c) 3/8 | d) 7/8
Total = 4+2+1+1 = 8. P(red) = 4/8 = 1/2. P(blue or green) = (2+1)/8 = 3/8. P(NOT yellow) = (8-1)/8 = 7/8.
2
a) 13/52 = 1/4 | b) 26/52 = 1/2 | c) 39/52 = 3/4
P(heart) = 13/52 = 1/4. P(red) = (13+13)/52 = 26/52 = 1/2. P(not spade) = (52-13)/52 = 39/52 = 3/4.
3
a) Likely | b) Impossible | c) Equally likely | d) Unlikely
0.9 is close to 1 (likely). 0 means impossible. 1/2 = 0.5 (equally likely). 0.15 is close to 0 (unlikely).
4
P(red) = 6/15 = 2/5 | P(blue) = 4/15 | Red is MORE likely
Total = 6+4+5 = 15. P(red) = 6/15 = 2/5 = 0.4. P(blue) = 4/15 ≈ 0.267. 0.4 > 0.267, so red is more likely.
Practice Worksheet Answers

Part A: Sample Spaces

1
{HH, HT, TH, TT} | 4 outcomes
Two coin flips: each flip has 2 outcomes, so 2 x 2 = 4 total outcomes.
2
{E, O} | 2 outcomes
Recording only even or odd, so just 2 possible outcomes.
3
{AH, AT, BH, BT, CH, CT} | 6 outcomes
3 spinner sections x 2 coin outcomes = 6 total outcomes.

Part B: Calculating Probability

4
a) 4/15 | b) 6/15 = 2/5 | c) 5/15 = 1/3 | d) 10/15 = 2/3 | e) 10/15 = 2/3
Total = 4+6+5 = 15. P(red) = 4/15. P(blue) = 6/15 = 2/5. P(green) = 5/15 = 1/3. P(red or blue) = (4+6)/15 = 10/15 = 2/3. P(not green) = 10/15 = 2/3.
5
a) 1/10 | b) 5/10 = 1/2 | c) 4/10 = 2/5 | d) 10/10 = 1 (certain)
a) Only one 7 out of 10. b) Even: 2,4,6,8,10 = 5/10. c) Greater than 6: 7,8,9,10 = 4/10. d) All numbers are 1-10, so P = 1.
6
4/52 = 1/13
4 Kings in 52 cards. P(King) = 4/52 = 1/13.
7
26/52 = 1/2
26 red cards (13 hearts + 13 diamonds) in 52 cards. P(red) = 26/52 = 1/2.

Part C: Interpreting Probability

#ProbabilityClassification
8P = 0Impossible
9P = 0.85Likely
10P = 1/2Equally likely
11P = 1Certain

Part D: Comparing Probabilities

12
P(red from A) = 3/10 = 0.3 | P(red from B) = 5/10 = 0.5 | Box B is more likely
Box A: 3 red out of 10 = 30%. Box B: 5 red out of 10 = 50%. 50% > 30%, so Box B.
13
A, B, C (Least to Most)
A: 1/6 ≈ 0.167. B: 1/2 = 0.5. C: 8/10 = 0.8. Order: 0.167 < 0.5 < 0.8.

Part E: Word Problems

14
Fraction: 7/10 | Decimal: 0.7 | Percent: 70%
Makes 7 out of 10. P = 7/10 = 0.7 = 70%.
15
Fraction: 7/10 | Decimal: 0.7
P(NOT rain) = 1 - 0.30 = 0.70 = 7/10.
16
P(boy) = 12/30 = 2/5
30 - 18 girls = 12 boys. P(boy) = 12/30 = 2/5 = 0.4 = 40%.

Part F: Tree Diagrams

17
a) 12 outcomes | b) 1/12 | c) 3/12 = 1/4
Coin (2) x Die (6) = 12 outcomes. P(H and 4) = 1/12. P(T and even) = P(T2, T4, T6) = 3/12 = 1/4.

Challenge

18
P(red then red) = 9/25
P(red) = 3/5. With replacement, P(red then red) = 3/5 x 3/5 = 9/25.
19
P(at least one blue) = 16/25
P(at least one blue) = 1 - P(no blue) = 1 - P(red then red) = 1 - 9/25 = 16/25.
FAST Practice Quiz Answers
1
B) 3/10
Total = 5+3+2 = 10 marbles. P(blue) = 3/10. A uses wrong total. C and D are wrong calculations.
2
B) 4/8 or 1/2
Odd numbers 1-8: 1, 3, 5, 7 = 4 numbers. P(odd) = 4/8 = 1/2.
3
C) It is unlikely to rain tomorrow.
0.35 is less than 0.5, so it's closer to "unlikely" than "equally likely." A is P=1, B is P=0, D is P=0.5.
4
Select: 0.75, 75%, 6/8
0.75 - Correct (3/4 = 0.75)
75% - Correct (3/4 = 75%)
0.34 - Incorrect (this is about 1/3)
6/8 - Correct (6/8 = 3/4)
34% - Incorrect (this is about 1/3)
5
D) 12
Coin has 2 outcomes, die has 6 outcomes. Total = 2 x 6 = 12 outcomes.
6
B) Event B, because 0.45 > 2/5
2/5 = 0.40. Since 0.45 > 0.40, Event B is more likely. Convert to same form to compare.
FAST Quiz Scoring Guide
ScoreInterpretationRecommended Action
6/6MasteryReady for compound probability and independent/dependent events
4-5/6Approaching MasteryReview specific areas - converting between forms or sample space counting
2-3/6DevelopingReteach with hands-on activities using actual dice, coins, and spinners
0-1/6Needs InterventionSmall group instruction starting with basic fraction concepts and counting

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FAST Success Kit | Grade 7 | FL B.E.S.T. Standards: MA.7.DP.2.1, MA.7.DP.2.2, MA.7.DP.2.3 | Answer Key - Teacher Use Only