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 Easy
One fair die rolled. What is P(getting 5)?
ExplanationP = 1/6. -
Q2 Easy
One fair die rolled. What is P(getting a number greater than 4)?
ExplanationFaces 5, 6: P = 2/6 = 1/3. -
Q3 Medium
Two dice rolled. What is P(sum equals 6)?
ExplanationFive pairs: (1,5),(2,4),(3,3),(4,2),(5,1). P = 5/36. -
Q4 Easy
Two dice rolled. What is P(sum equals 12)?
ExplanationOnly (6,6): P = 1/36. -
Q5 Easy
One die rolled. What is P(getting 1 or 6)?
ExplanationMutually exclusive: P = 1/6 + 1/6 = 1/3. -
Q6 Medium
Two dice rolled. What is P(sum less than 5)?
ExplanationSums 2,3,4: 1+2+3 = 6 outcomes. P = 6/36 = 1/6. -
Q7 Medium
Two dice rolled. What is P(sum equals 9)?
ExplanationFour pairs: (3,6),(4,5),(5,4),(6,3). P = 4/36 = 1/9.
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Q8 Medium
One die rolled twice. What is P(same number both times)?
ExplanationSix doubles out of 36: P = 6/36 = 1/6. -
Q9 Hard
Two dice rolled. What is P(at least one die shows 6)?
Explanation1 − P(no six) = 1 − (5/6)^2 = 11/36. -
Q10 Medium
One die rolled. What is P(composite number)?
ExplanationComposite faces: 4, 6. P = 2/6 = 1/3. -
Q11 Medium
Two dice rolled. What is P(sum equals 4)?
ExplanationThree pairs: (1,3),(2,2),(3,1). P = 3/36 = 1/12. -
Q12 Easy
Two dice rolled. What is P(first die 3 and second die 5)?
ExplanationOne specific ordered pair: P = 1/36. -
Q13 Hard
Two dice rolled. What is P(sum is a multiple of 3)?
ExplanationSums 3,6,9,12: 2+5+4+1 = 12 outcomes. P = 12/36 = 1/3. -
Q14 Easy
One die rolled. What is P(number at most 3)?
ExplanationFaces 1, 2, 3: P = 3/6 = 1/2.
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DS1 Easy
What is P(sum equals 7 when two dice are rolled)?
Statement ITwo fair dice are rolled.
Statement IISix ordered pairs give sum 7.
ExplanationNeed both: P = 6/36 = 1/6. -
DS2 Easy
What is P(getting 6 on one die roll)?
Statement IA fair six-sided die is rolled.
Statement IIEach face has probability 1/6.
ExplanationEach alone gives P = 1/6.
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DS3 Medium
What is P(sum at least 11 when two dice are rolled)?
Statement ITwo dice are rolled.
Statement IIThree outcomes give sum 11 or 12.
ExplanationNeed both: P = 3/36 = 1/12. -
DS4 Hard
What is P(at least one six when two dice are rolled)?
Statement ITwo fair dice are rolled.
Statement IIP(no six on either die) = 25/36.
ExplanationStatement II alone: P = 1 − 25/36 = 11/36.