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This question is commonly asked for Data Scientist candidates at PayPal during technical interviews.

Calculate Probability of Heads in Coin Flip Experiment

Quick Overview

This interview question evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer for Calculate Probability of Heads in Coin Flip Experiment states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

Calculate Probability of Heads in Coin Flip Experiment

Coin Flips: Counting and Binomial Probabilities

Context

Assume 10 independent flips of a fair coin (probability of heads p = 0.5 for each flip). Each length-10 outcome sequence is equally likely.

Question

Calculate:

(a) The total number of possible outcome sequences.

(b) The probability of exactly 3 heads.

Constraints & Assumptions

Preserve the scope, facts, inputs, and requested outputs from the prompt above.
If the prompt leaves a detail unspecified, state a reasonable assumption before relying on it.
Keep the answer interview-ready: concise enough to present, but concrete enough to implement or evaluate.

Clarifying Questions to Ask Guidance

Clarify the random variables, distributional assumptions, independence assumptions, and desired output.
Show enough derivation for the interviewer to follow the reasoning.
Explain how you would validate the result with simulation or sensitivity checks.

What a Strong Answer Covers Guidance

A correct setup with definitions, formulas, and boundary conditions.
A step-by-step derivation or estimation plan.
Interpretation of the result, including uncertainty and practical limitations.
Checks for assumptions, edge cases, and numerical stability.

Follow-up Questions Guidance

How would the result change if the assumptions were relaxed?
Can you verify the answer with a simulation?
What is the most likely source of estimation error?

Quick Overview

Question

Calculate:

(a) The total number of possible outcome sequences.

(b) The probability of exactly 3 heads.

Constraints & Assumptions

Preserve the scope, facts, inputs, and requested outputs from the prompt above.

If the prompt leaves a detail unspecified, state a reasonable assumption before relying on it.

Keep the answer interview-ready: concise enough to present, but concrete enough to implement or evaluate.

Clarifying Questions to Ask Guidance

Clarify the random variables, distributional assumptions, independence assumptions, and desired output.

Show enough derivation for the interviewer to follow the reasoning.

Explain how you would validate the result with simulation or sensitivity checks.

What a Strong Answer Covers Guidance

A correct setup with definitions, formulas, and boundary conditions.

A step-by-step derivation or estimation plan.

Interpretation of the result, including uncertainty and practical limitations.

Checks for assumptions, edge cases, and numerical stability.

Follow-up Questions Guidance

How would the result change if the assumptions were relaxed?

Can you verify the answer with a simulation?

What is the most likely source of estimation error?

Calculate Probability of Heads in Coin Flip Experiment

Quick Overview

Calculate Probability of Heads in Coin Flip Experiment

Calculate Probability of Heads in Coin Flip Experiment

Coin Flips: Counting and Binomial Probabilities

Context

Question

Constraints & Assumptions

Clarifying Questions to Ask Guidance

What a Strong Answer Covers Guidance

Follow-up Questions Guidance

Write your answer

Calculate Probability of Heads in Coin Flip Experiment

Quick Overview

Calculate Probability of Heads in Coin Flip Experiment

Calculate Probability of Heads in Coin Flip Experiment

Coin Flips: Counting and Binomial Probabilities

Context

Question

Constraints & Assumptions

Clarifying Questions to Ask Guidance

What a Strong Answer Covers Guidance

Follow-up Questions Guidance

Write your answer