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Microsoft·Data Analyst·Technical Phone Screen·Intermediate

IntermediatePrefer not to say
Jun 2026

Summary

Interviewed at Microsoft, got a probability question that felt more like a math class than a technical screen. Short and straightforward, but I second-guessed myself more than I should have.

Questions Asked (1)

Q1

When rolling two fair dice, what is the probability that the sum is less than 12?

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Author's notes

I overcomplicated this.

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AI HintsAI Generated

Suggested Approach

Recognize that the sum of two fair dice ranges from 2 to 12, so the only way to get a sum not less than 12 is to roll a 12 (6+6). Calculate the probability of rolling a 12 (1/36) and subtract from 1 to get 35/36. Alternatively, count all 36 outcomes and subtract the one outcome that sums to 12.

Pro tip: Show that you can solve it both by complement and by direct enumeration, and mention that this is a common trick question where the obvious answer (11/12) is wrong because it ignores the distribution of sums.

1. Identify the sample space

State that there are 36 equally likely outcomes when rolling two fair dice (6 sides each).

2. Define the event

Clarify that 'sum less than 12' means sum ≤ 11, and the complement is sum ≥ 12, which only occurs for sum = 12.

3. Count favorable outcomes

Count the number of outcomes where sum < 12: all except (6,6), so 35 outcomes.

4. Compute probability

Divide favorable outcomes by total outcomes: 35/36.

5. Verify with complement

Alternatively, compute P(sum=12) = 1/36, then P(sum<12) = 1 - 1/36 = 35/36.

Key Points to Mention

  • Total number of outcomes is 36 (6x6).
  • The only sum not less than 12 is 12 itself.
  • Only one outcome gives sum 12: (6,6).
  • Probability of sum 12 is 1/36.
  • Therefore, probability of sum less than 12 is 1 - 1/36 = 35/36.
  • Common mistake: assuming each sum from 2 to 12 is equally likely.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.