Probability Practice Problems
Master probability concepts from basic chance calculations to compound events. These problems build intuition for understanding likelihood in real-world situations.
Skills You'll Practice
- Calculating simple probability
- Understanding experimental vs theoretical probability
- Working with compound events
- Using tree diagrams
- Understanding independent and dependent events
- Calculating expected value (intro)
Simple Probability
EasyA die is rolled. P(getting a 4) = ?
💡 Show Hint
1 favorable outcome out of 6 possible
✓ Show Answer
1/6
A bag has 3 red and 7 blue marbles. P(red) = ?
💡 Show Hint
3 red out of 10 total
✓ Show Answer
3/10 or 0.3
A coin is flipped. P(heads) = ?
💡 Show Hint
Equally likely outcomes
✓ Show Answer
1/2 or 0.5
Compound Probability
MediumP(rolling a 6 on a die AND flipping heads) = ?
💡 Show Hint
Independent events: multiply probabilities
✓ Show Answer
1/12
A die is rolled. P(even OR greater than 4) = ?
💡 Show Hint
Even: 2,4,6. >4: 5,6. Union: 2,4,5,6
✓ Show Answer
4/6 or 2/3
Two cards drawn with replacement. P(both red) = ?
💡 Show Hint
P(red) × P(red) = 1/2 × 1/2
✓ Show Answer
1/4
Dependent Events & Applications
HardTwo cards drawn WITHOUT replacement. P(both aces) = ?
💡 Show Hint
(4/52) × (3/51)
✓ Show Answer
12/2652 or 1/221
A bag has 5 red, 3 blue balls. If 2 drawn without replacement, P(both red) = ?
💡 Show Hint
(5/8) × (4/7)
✓ Show Answer
20/56 or 5/14
Expected value: Win $10 on heads, lose $8 on tails. E(X) = ?
💡 Show Hint
(1/2)(10) + (1/2)(-8)
✓ Show Answer
$1
Pro Tips
- 💡Probability = favorable outcomes / total possible outcomes
- 💡Probability ranges from 0 (impossible) to 1 (certain)
- 💡Independent events: P(A and B) = P(A) × P(B)
- 💡For "without replacement," probabilities change after each draw
Curriculum Alignment
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