Lyft·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

May 2026

Summary

Lyft data science interview with a probability question that sounds deceptively simple but trips you up if you rush the setup.

Questions Asked (1)

N riders each receive a discount coupon, and each rider independently uses their coupon with probability P. What is the probability that at least one coupon gets used?

Product Analytics & MetricsA/B Testing & Experimentation

Author's notes

I jumped straight to 1 minus (1-P)^N which is right, but I fumbled explaining why for a second.

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AI HintsAI Generated

Suggested Approach

Recognize that the event of interest is 'at least one coupon used', which is the complement of 'no coupons used'. Compute the probability that no rider uses their coupon, then subtract from 1 to get the desired probability.

Pro tip: Connect the result to Lyft's business context: this probability represents the expected redemption rate, which is crucial for evaluating coupon campaign effectiveness and ROI.

1. Define the event and its complement

Let A be the event that at least one coupon is used. Then A^c is the event that no coupons are used.

2. Compute probability of no coupons used

Since riders are independent, the probability that a single rider does not use their coupon is (1 - P). For N riders, the probability that none use their coupon is (1 - P)^N.

3. Apply complement rule

The probability that at least one coupon is used is 1 - (1 - P)^N.

4. Interpret in business context

Explain that this formula gives the expected redemption rate for a coupon campaign, which can inform decisions about coupon distribution and budget allocation.

Key Points to Mention

Independence assumption: each rider's decision is independent of others.
Complement rule: P(at least one) = 1 - P(none).
Binomial distribution: number of coupons used follows Binomial(N, P).
Business relevance: expected redemption rate, campaign ROI, and A/B testing metrics.
Edge cases: if P=0, probability is 0; if P=1, probability is 1.
Scalability: as N increases, probability approaches 1 if P>0.

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