Practice Questions
Concept Explanation
An event is a set of outcomes from a sample space. The probability of an event sums favourable equally likely outcomes and divides by the total.
Key Rules
- Sample space S = all possible outcomes
- P(E) = n(E) / n(S) when outcomes are equally likely
- P(E) + P(not E) = 1
Example
Two dice rolled: 36 outcomes. Event sum = 7 has 6 outcomes. P(sum 7) = 6/36 = 1/6.
Common Trap
Define the sample space first. Rolling two dice has 36 ordered outcomes, not 11 sums.
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Q1 Easy
Two fair dice are rolled. How many outcomes are in the sample space?
ExplanationEach die has 6 outcomes: 6 × 6 = 36. -
Q2 Medium
Two dice rolled. What is P(sum equals 7)?
ExplanationSix pairs give sum 7: P = 6/36 = 1/6. -
Q3 Easy
Two dice rolled. What is P(sum equals 2)?
ExplanationOnly (1,1) gives sum 2. P = 1/36. -
Q4 Easy
A card is drawn from a standard 52-card deck. What is P(king)?
Explanation4 kings in 52 cards: P = 4/52 = 1/13. -
Q5 Medium
Two dice rolled. What is P(sum is even)?
Explanation18 even-sum outcomes out of 36: P = 1/2. -
Q6 Medium
A letter is chosen at random from the word PROBABILITY. What is P(vowel)?
ExplanationVowels O, A, I, I: 4 out of 11 letters. -
Q7 Medium
Two dice rolled. What is P(doubles)?
ExplanationSix doubles out of 36: P = 6/36 = 1/6.
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Q8 Easy
From digits 1, 2, 3, 4, 5 one digit is chosen. What is P(even digit)?
ExplanationEven digits 2, 4: P = 2/5. -
Q9 Hard
Two dice rolled. What is P(sum at least 11)?
ExplanationSums 11 or 12: (5,6),(6,5),(6,6) = 3 outcomes. P = 3/36 = 1/12. -
Q10 Hard
A day is chosen at random from a non-leap year. What is P(Sunday)?
Explanation52 Sundays in 365 days: P = 52/365. -
Q11 Medium
Two dice rolled. What is P(sum equals 8)?
ExplanationFive pairs give sum 8. P = 5/36. -
Q12 Easy
One card drawn. What is P(red card)?
Explanation26 red cards: P = 26/52 = 1/2. -
Q13 Easy
Three coins tossed. How many outcomes in the sample space?
Explanation2^3 = 8 outcomes. -
Q14 Hard
Two dice rolled. What is P(product is odd)?
ExplanationBoth dice odd: 3 × 3 = 9 outcomes. P = 9/36 = 1/4.
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DS1 Medium
What is P(sum equals 7 when two dice are rolled)?
Statement ITwo fair dice are rolled.
Statement IIThere are 6 outcomes with sum 7 out of 36.
ExplanationNeed both to compute P = 6/36 = 1/6. -
DS2 Easy
What is P(drawing a king from a deck)?
Statement IA standard 52-card deck is used.
Statement IIThere are 4 kings in the deck.
ExplanationEach alone gives P = 4/52 = 1/13.
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DS3 Easy
How many outcomes are in the sample space when two dice are rolled?
Statement IEach die has 6 faces.
Statement IIOutcomes are ordered pairs.
ExplanationNeed both: 6 × 6 = 36 outcomes. -
DS4 Medium
What is P(sum is even when two dice are rolled)?
Statement I36 equally likely ordered outcomes exist.
Statement IIExactly 18 of them have an even sum.
ExplanationEach alone gives P = 18/36 = 1/2.