Practice Questions
Concept Explanation
Probability measures how likely an event is, on a scale from 0 to 1. For equally likely outcomes, probability is the ratio of favourable outcomes to total outcomes.
Key Formula
- P(E) = Number of favourable outcomes / Total number of outcomes
- 0 ≤ P(E) ≤ 1
- P(certain event) = 1; P(impossible event) = 0
Example
A fair die has 6 equally likely faces. P(getting 4) = 1/6.
Common Trap
Count only equally likely outcomes. If outcomes are not equally likely, simple counting does not give correct probability.
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Q1 Easy
A bag has 3 red and 7 blue balls. One ball is drawn at random. What is P(red)?
ExplanationFavourable = 3, total = 10. P(red) = 3/10. -
Q2 Easy
A fair die is rolled once. What is P(getting an even number)?
ExplanationEven faces: 2, 4, 6. P = 3/6 = 1/2. -
Q3 Easy
From 100 lottery tickets, 5 are winners. One ticket is drawn. What is P(winning)?
ExplanationP = 5/100 = 1/20. -
Q4 Easy
A spinner has 8 equal sections, 3 are green. What is P(landing on green)?
ExplanationP = 3/8. -
Q5 Easy
In a class of 12 students, 4 wear glasses. One student is picked at random. What is P(wearing glasses)?
ExplanationP = 4/12 = 1/3. -
Q6 Easy
An urn has 5 white and 2 black balls. What is P(drawing a black ball)?
ExplanationP = 2/7. -
Q7 Easy
A fair coin is tossed once. What is P(getting heads)?
ExplanationTwo equally likely outcomes: P(H) = 1/2.
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Q8 Medium
Cards numbered 1 to 20 are shuffled. What is P(picking a multiple of 5)?
ExplanationMultiples of 5: 5, 10, 15, 20. P = 4/20 = 1/5. -
Q9 Medium
A box has 6 apples and 4 oranges. One fruit is picked. What is P(not an apple)?
ExplanationP(orange) = 4/10 = 2/5. -
Q10 Medium
50 balls: 10 red, 15 blue, 25 green. What is P(blue)?
ExplanationP = 15/50 = 3/10. -
Q11 Medium
A bag has letters A, A, B, C (4 letters). What is P(drawing A)?
ExplanationP = 2/4 = 1/2. -
Q12 Medium
36 students sit an exam; 12 score above 80. One student is chosen. What is P(score above 80)?
ExplanationP = 12/36 = 1/3. -
Q13 Medium
A fair die is rolled. What is P(getting a prime number)?
ExplanationPrimes on a die: 2, 3, 5. P = 3/6 = 1/2. -
Q14 Hard
A bag has 2 red, 3 green, and 5 yellow balls. What is P(not yellow)?
ExplanationNon-yellow = 5, total = 10. P = 5/10 = 1/2.
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DS1 Easy
What is P(drawing a red ball from the bag)?
Statement IThe bag has 4 red and 6 blue balls.
Statement IIThere are 10 balls in total.
ExplanationEach statement alone: 4 red out of 10 gives P = 4/10 = 2/5. -
DS2 Easy
What is P(getting an even number on a die roll)?
Statement IA fair six-sided die is used.
Statement IIEven outcomes are 2, 4, and 6.
ExplanationEach alone gives 3 favourable out of 6: P = 1/2.
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DS3 Medium
What is P(winning a lottery draw)?
Statement I200 tickets are sold and 8 are winning tickets.
Statement IIExactly one ticket is drawn at random.
ExplanationNeed both: P = 8/200 = 1/25. -
DS4 Medium
What is P(landing on green on a spinner)?
Statement IThe spinner has 5 green sections out of 20 equal sections.
Statement IIAll sections are equally likely.
ExplanationStatement I alone: P = 5/20 = 1/4.