Practice Questions
Concept Explanation
Drawing balls from a bag uses P(E) = favourable / total when each ball is equally likely. With replacement, totals stay fixed; without replacement, totals shrink.
Key Rules
- With replacement: probabilities stay the same each draw
- Without replacement: adjust counts after each draw
- Two draws without replacement: multiply sequential probabilities
Example
Bag: 3 red, 2 blue. P(red) = 3/5. Without replacement, P(second red | first red) = 2/4.
Common Trap
Check whether drawing is with or without replacement before computing.
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Q1 Easy
A bag has 4 red and 6 blue balls. One ball drawn. What is P(red)?
ExplanationP = 4/10 = 2/5. -
Q2 Easy
Bag: 5 white, 3 black. One ball drawn. What is P(black)?
ExplanationP = 3/8. -
Q3 Easy
Bag: 2 red, 2 green, 1 yellow. What is P(yellow)?
ExplanationP = 1/5. -
Q4 Medium
Bag: 7 red, 3 blue. Two balls drawn with replacement. What is P(both red)?
ExplanationP = (7/10) × (7/10) = 49/100. -
Q5 Medium
Bag: 3 red, 2 blue. Two balls without replacement. What is P(both red)?
ExplanationP = (3/5) × (2/4) = 6/20 = 3/10. -
Q6 Easy
Bag: 6 red, 4 blue. One ball drawn. What is P(not red)?
ExplanationP(blue) = 4/10 = 2/5. -
Q7 Easy
Bag: 8 balls numbered 1–8. What is P(even number)?
ExplanationEven: 2,4,6,8. P = 4/8 = 1/2.
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Q8 Medium
Bag: 5 red, 5 blue. Two draws with replacement. What is P(first red, second blue)?
ExplanationP = (1/2) × (1/2) = 1/4. -
Q9 Easy
Bag: 4 red, 1 blue. One ball drawn. What is P(blue)?
ExplanationP = 1/5. -
Q10 Medium
Bag: 3 red, 3 blue, 3 green. What is P(not green)?
ExplanationP = 6/9 = 2/3. -
Q11 Easy
Bag: 10 balls, 4 defective. What is P(non-defective)?
ExplanationP = 6/10 = 3/5. -
Q12 Hard
Bag: 2 red, 3 blue, 5 white. Two draws without replacement. What is P(first red, second blue)?
ExplanationP = (2/10) × (3/9) = 6/90 = 1/15. -
Q13 Hard
Bag: 6 red, 2 blue. Two draws with replacement. What is P(at least one blue)?
Explanation1 − (6/8)^2 = 1 − 36/64 = 7/16. -
Q14 Medium
Bag: 1 red, 2 blue, 3 green. What is P(red or green)?
ExplanationMutually exclusive: (1+3)/6 = 4/6 = 2/3.
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DS1 Easy
What is P(drawing a red ball)?
Statement IThe bag has 5 red and 5 blue balls.
Statement IIThere are 10 balls in total.
ExplanationEach alone gives P = 5/10 = 1/2. -
DS2 Medium
What is P(both draws are red with replacement)?
Statement IThe bag has 4 red and 6 blue balls.
Statement IITwo balls are drawn with replacement.
ExplanationNeed both: P = (4/10)^2 = 16/100 = 4/25.
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DS3 Easy
What is P(drawing a black ball)?
Statement IA bag has 7 white and 3 black balls.
Statement IIOne ball is drawn at random.
ExplanationNeed both: P = 3/10. -
DS4 Hard
What is P(both red without replacement)?
Statement IA bag has 3 red and 2 blue balls.
Statement IITwo balls are drawn without replacement.
ExplanationNeed both: P = (3/5) × (2/4) = 3/10.