Practice Questions
Concept Explanation
A standard fair die has faces 1 through 6, each with probability 1/6. With two dice, list ordered pairs for equally likely outcomes.
Key Rules
- One die: P(any face) = 1/6
- Two dice: 36 ordered outcomes
- Sum probabilities differ — sum 7 is most likely at 6/36
Example
P(sum 7) = 6/36 = 1/6; P(sum 12) = 1/36.
Common Trap
Do not assume all sums from 2 to 12 are equally likely.
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Q1 EasyOne fair die is rolled. What is the probability of getting 5?ExplanationP(E) = favourable / total. Favourable face 5 → 1 out of 6. P = 1/6. Hence the answer is 1/6.
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Q2 EasyOne fair die is rolled. What is the probability of getting a number greater than 4?ExplanationP(E) = favourable / total. Faces greater than 4: 5, 6 → 2 out of 6. P = 2/6 = 1/3. Hence the answer is 1/3.
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Q3 EasyA die is thrown. What is the probability of getting an odd number?ExplanationP(E) = favourable / total. Odd faces: 1, 3, 5 → 3 out of 6. P = 3/6 = 1/2. Hence the answer is 1/2.
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Q4 EasyA die is thrown. What is the probability of getting a multiple of 3?ExplanationP(E) = favourable / total. Multiples of 3: 3, 6 → 2 out of 6. P = 2/6 = 1/3. Hence the answer is 1/3.
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Q5 EasyTwo dice are rolled. What is the probability that the sum equals 12?ExplanationP(E) = favourable / total. Only (6,6) → 1 out of 36. P = 1/36. Hence the answer is 1/36.
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Q6 EasyOne fair die is rolled. What is the probability of getting a number at most 3?ExplanationP(E) = favourable / total. Faces 1, 2, 3 → 3 out of 6. P = 3/6 = 1/2. Hence the answer is 1/2.
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Q7 MediumTwo dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?ExplanationP(E) = favourable / total. Total = 36. Odd product only if both odd: 3 × 3 = 9. Even product = 36 − 9 = 27. P = 27/36 = 3/4. Hence the answer is 3/4.
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Q8 MediumTwo dice are rolled. What is the probability that the sum equals 6?ExplanationP(E) = favourable / total. Sum 6: (1,5),(2,4),(3,3),(4,2),(5,1) → 5. P = 5/36. Hence the answer is 5/36.
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Q9 MediumTwo dice are tossed. What is the probability that the sum is 9?ExplanationP(E) = favourable / total. Sum 9: (3,6),(4,5),(5,4),(6,3) → 4 out of 36. P = 4/36 = 1/9. Hence the answer is 1/9.
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Q10 MediumTwo dice are rolled. What is the probability that the sum is less than 5?ExplanationP(E) = favourable / total. Sums 2, 3, 4: 1 + 2 + 3 = 6 outcomes. P = 6/36 = 1/6. Hence the answer is 1/6.
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Q11 MediumTwo dice are tossed. What is the probability that the sum is 7?ExplanationP(E) = favourable / total. Sum 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) → 6 out of 36. P = 6/36 = 1/6. Hence the answer is 1/6.
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Q12 MediumTwo dice are thrown. What is the probability that both dice show the same number?ExplanationP(E) = favourable / total. Same number (doubles): (1,1),(2,2),(3,3),(4,4),(5,5),(6,6) → 6 out of 36. P = 6/36 = 1/6. Hence the answer is 1/6.
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Q13 HardTwo dice are tossed. The probability that the total score is a prime number is:ExplanationP(E) = favourable / total. Total = 36. Prime sums 2,3,5,7,11 have 1+2+4+6+2 = 15 outcomes. P = 15/36 = 5/12. Hence the answer is 5/12.
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Q14 HardTwo dice are rolled. What is the probability that at least one die shows 6?ExplanationP(E) = 1 − P(no six). P(no six) = 5/6 × 5/6 = 25/36. P(at least one six) = 1 − 25/36 = 11/36. Hence the answer is 11/36.
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DS1 Easy
What is the probability that the sum equals 7 when two dice are rolled?
Statement ITwo fair dice are rolled.
Statement IIExactly six ordered pairs give sum 7.
ExplanationStatement I alone lacks the favourable count. Statement II alone lacks the total number of outcomes. Together: total = 36, favourable = 6, P = 6/36 = 1/6. Both needed. Answer: C. -
DS2 Easy
What is the probability of getting 6 on one die roll?
Statement IA fair six-sided die is rolled.
Statement IIEach face has probability 1/6.
ExplanationStatement I alone: one face out of six → P = 1/6. Statement II alone directly gives P = 1/6. Each alone is sufficient. Answer: D.
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DS3 Medium
For the probability that the sum is at least 11 when two dice are rolled. What is that probability?
Statement ITwo fair dice are rolled (36 outcomes).
Statement IIExactly three outcomes give sum 11 or 12.
ExplanationStatement I alone lacks the favourable count. Statement II alone lacks confirmation of total 36. Together: P = 3/36 = 1/12. Both needed. Answer: C. -
DS4 Hard
For the probability of at least one six when two dice are rolled. What is that probability?
Statement ITwo fair dice are rolled.
Statement IIThe probability of no six on either die is 25/36.
ExplanationStatement I alone requires further counting. Statement II alone: P(at least one six) = 1 − 25/36 = 11/36. Answer: B.