Fillable Online Probability Worksheet 3 Compound Events Name Fax ... - Free Printable

Let’s solve each problem step by step. We’ll break them into sections.

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## SECTION 1: Marbles — WITHOUT Replacement

Bag contains:
- Green = 2
- Brown = 9
- Yellow = 7
- Blue = 4
→ Total marbles = 2 + 9 + 7 + 4 = 22

Since marbles are not replaced, the total number of marbles decreases after each draw.

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1. P(brown, then yellow)

- P(first brown) = 9/22
- After removing one brown, total marbles = 21, yellow still = 7
- P(yellow second) = 7/21 = 1/3

→ P = (9/22) × (7/21) = (9/22) × (1/3) = 9/66 = 3/22

✔ Answer: 3/22

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2. P(green, then blue)

- P(green first) = 2/22 = 1/11
- After removing green, total = 21, blue = 4
- P(blue second) = 4/21

→ P = (2/22) × (4/21) = (1/11) × (4/21) = 4/231

✔ Answer: 4/231

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3. P(yellow, then yellow)

- P(first yellow) = 7/22
- After removing one yellow, yellow left = 6, total = 21
- P(second yellow) = 6/21 = 2/7

→ P = (7/22) × (6/21) = (7/22) × (2/7) = 14/154 = 1/11

✔ Answer: 1/11

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4. P(blue, then blue)

- P(first blue) = 4/22 = 2/11
- After removing one blue, blue left = 3, total = 21
- P(second blue) = 3/21 = 1/7

→ P = (4/22) × (3/21) = (2/11) × (1/7) = 2/77

✔ Answer: 2/77

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5. P(green, then NOT blue)

- P(green first) = 2/22 = 1/11
- After removing green, total = 21
- NOT blue = all except blue → 21 - 4 = 17 (since 4 blue remain)
→ P(not blue second) = 17/21

→ P = (2/22) × (17/21) = (1/11) × (17/21) = 17/231

✔ Answer: 17/231

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6. P(brown, then NOT green)

- P(brown first) = 9/22
- After removing brown, total = 21
- NOT green = 21 - 2 = 19 (green still 2, since we removed a brown)

→ P(not green second) = 19/21

→ P = (9/22) × (19/21) = 171/462

Simplify: divide numerator and denominator by 3 → 57/154

✔ Answer: 57/154

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## SECTION 2: Marbles — WITH Replacement

Now, marble is replaced, so total remains 22 for every draw.

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7. P(brown, then yellow)

- P(brown) = 9/22
- P(yellow) = 7/22

→ P = (9/22) × (7/22) = 63/484

✔ Answer: 63/484

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8. P(green, then blue)

- P(green) = 2/22 = 1/11
- P(blue) = 4/22 = 2/11

→ P = (2/22) × (4/22) = (1/11) × (2/11) = 2/121

✔ Answer: 2/121

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9. P(yellow, then yellow)

- P(yellow) = 7/22 both times

→ P = (7/22) × (7/22) = 49/484

✔ Answer: 49/484

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10. P(blue, then blue)

- P(blue) = 4/22 = 2/11 both times

→ P = (4/22) × (4/22) = (2/11) × (2/11) = 4/121

✔ Answer: 4/121

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11. P(green, then NOT blue)

- P(green) = 2/22 = 1/11
- P(not blue) = 1 - P(blue) = 1 - 4/22 = 18/22 = 9/11

→ P = (2/22) × (18/22) = (1/11) × (9/11) = 9/121

✔ Answer: 9/121

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12. P(brown, then NOT green)

- P(brown) = 9/22
- P(not green) = 1 - P(green) = 1 - 2/22 = 20/22 = 10/11

→ P = (9/22) × (20/22) = 180/484

Simplify: divide by 4 → 45/121

✔ Answer: 45/121

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## SECTION 3: Die and Spinner

- Die: 6-sided → outcomes 1,2,3,4,5,6 → each has prob 1/6
- Spinner: 4 equal regions: A, B, C, D → each has prob 1/4
- Events are independent → multiply probabilities

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13. P(4 and A)

- P(4 on die) = 1/6
- P(A on spinner) = 1/4

→ P = (1/6) × (1/4) = 1/24

✔ Answer: 1/24

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14. P(even number and C)

Even numbers on die: 2,4,6 → 3 out of 6 → P(even) = 3/6 = 1/2
P(C) = 1/4

→ P = (1/2) × (1/4) = 1/8

✔ Answer: 1/8

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15. P(2 or 5 and B or D)

- P(2 or 5) = 2/6 = 1/3
- P(B or D) = 2/4 = 1/2

→ P = (1/3) × (1/2) = 1/6

✔ Answer: 1/6

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16. P(a number less than 5 and B, C, or D)

Numbers less than 5: 1,2,3,4 → 4 out of 6 → P = 4/6 = 2/3
B, C, or D → 3 out of 4 → P = 3/4

→ P = (2/3) × (3/4) = 6/12 = 1/2

✔ Answer: 1/2

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## SECTION 4: M&Ms — WITHOUT Replacement (eaten)

Bag contains:
- Red = 5
- Brown = 3
- Yellow = 6
- Blue = 2
→ Total = 5+3+6+2 = 16

Marbles are eaten → no replacement

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17. P(brown, then yellow, then red)

- P(brown first) = 3/16
- After brown removed: total = 15, yellow = 6 → P(yellow) = 6/15 = 2/5
- After yellow removed: total = 14, red = 5 → P(red) = 5/14

→ P = (3/16) × (6/15) × (5/14)

Calculate step by step:

= (3/16) × (2/5) × (5/14) [since 6/15 = 2/5]

Notice 5 cancels: (3/16) × (2/1) × (1/14) = (3×2)/(16×14) = 6/224 = 3/112

✔ Answer: 3/112

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18. P(red, then red, then blue)

- P(red first) = 5/16
- After red removed: red = 4, total = 15 → P(red) = 4/15
- After another red: total = 14, blue = 2 → P(blue) = 2/14 = 1/7

→ P = (5/16) × (4/15) × (2/14)

= (5/16) × (4/15) × (1/7)

Multiply numerators: 5×4×1 = 20
Denominators: 16×15×7 = 1680

→ 20/1680 = 1/84

✔ Answer: 1/84

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19. P(yellow, then yellow, then not blue)

- P(yellow first) = 6/16 = 3/8
- After yellow: yellow = 5, total = 15 → P(yellow) = 5/15 = 1/3
- After second yellow: total = 14, blue = 2 → not blue = 12 → P(not blue) = 12/14 = 6/7

→ P = (6/16) × (5/15) × (12/14)

= (3/8) × (1/3) × (6/7)

Cancel 3: (1/8) × (1) × (6/7) = 6/56 = 3/28

✔ Answer: 3/28

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20. P(brown, then brown, then not red)

- P(brown first) = 3/16
- After brown: brown = 2, total = 15 → P(brown) = 2/15
- After second brown: total = 14, red = 5 → not red = 9 → P(not red) = 9/14

→ P = (3/16) × (2/15) × (9/14)

Multiply numerators: 3×2×9 = 54
Denominators: 16×15×14 = 3360

→ 54/3360

Simplify: divide numerator and denominator by 6 → 9/560

✔ Answer: 9/560

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## ✔ FINAL ANSWERS:

1. 3/22
2. 4/231
3. 1/11
4. 2/77
5. 17/231
6. 57/154
7. 63/484
8. 2/121
9. 49/484
10. 4/121
11. 9/121
12. 45/121
13. 1/24
14. 1/8
15. 1/6
16. 1/2
17. 3/112
18. 1/84
19. 3/28
20. 9/560

Let me know if you’d like these in decimal form or simplified differently!