Let’s go through each problem one by one. I’ll solve them step by step, check my math, and then give you the final answers.
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Problem 1:
Out of 20 students, teacher picks you first, then Kim second — without replacement.
- P(you) = 1/20
- After you’re picked, 19 students left → P(Kim) = 1/19
- Multiply: (1/20) × (1/19) = 1/380
✔
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Problem 2:
Flip a fair coin twice. Want heads then tails.
- P(heads) = 1/2
- P(tails) = 1/2 (coin doesn’t change — independent)
- Multiply: (1/2) × (1/2) = 1/4
✔
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Problem 3:
Tom has 4 navy + 6 black socks = 10 total. Picks 2 socks without replacement. Want both navy.
- First pick: P(navy) = 4/10
- Second pick: now 3 navy left, 9 total → P(navy) = 3/9
- Multiply: (4/10) × (3/9) = 12/90 = simplify → divide numerator and denominator by 6 → 2/15
✔
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Problem 4:
Dave has 2 root beer + 4 cola = 6 glasses. Drinks 2 at random. Want both cola.
- First pick: P(cola) = 4/6
- Second pick: 3 cola left, 5 total → P(cola) = 3/5
- Multiply: (4/6) × (3/5) = 12/30 = simplify → divide by 6 → 2/5
✔
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Problem 5:
Steve picks a marble from bag with 5 red, 3 yellow, 2 green = 10 total. He puts it back. Then Sam picks. Want both to pick yellow.
- Since he replaces it, probabilities stay same.
- P(yellow) for Steve = 3/10
- P(yellow) for Sam = 3/10
- Multiply: (3/10) × (3/10) = 9/100
✔
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Problem 6:
Bowl has 4 tangerines + 5 clementines = 9 total fruit. John picks one, then Pam picks from remaining. Want John gets tangerine AND Pam gets clementine.
- P(John picks tangerine) = 4/9
- Now 8 fruits left: 3 tangerines, 5 clementines → P(Pam picks clementine) = 5/8
- Multiply: (4/9) × (5/8) = 20/72
- Simplify: divide numerator and denominator by 4 → 5/18
✔
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All calculations checked and correct.
Final Answer:
1) 1/380
2) 1/4
3) 2/15
4) 2/5
5) 9/100
6) 5/18
Parent Tip: Review the logic above to help your child master the concept of independent and dependent probability worksheet with answer key.
