Assess Probability of Heads in Coin Tosses

Quick Overview

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

Assess Probability of Heads in Coin Tosses

Company: Upstart

Role: Data Scientist

Category: Statistics & Math

Difficulty: easy

Interview Round: Onsite

##### Scenario HR screening for data-science role; assessing basic probability knowledge ##### Question A coin is tossed N times into a cup. Assuming each toss is independent and fair, what is the probability of observing exactly k heads? How would your answer change if the coin is biased with probability p of heads? For a variable X~N(μ,σ²), derive P(a<X<b) and explain how to standardise a normal variable. ##### Hints Use binomial pmf and standard normal Z-score transformation.

Quick Answer: Assess Probability of Heads in Coin Tosses evaluates statistical assumptions, formulas, estimation strategy, uncertainty, edge cases, and interpretation in a realistic interview setting. A strong answer states assumptions, handles edge cases, explains trade-offs, and shows how to validate the result clearly.

|Home/Statistics & Math/Upstart
Upstart logo
Upstart
Aug 4, 2025, 10:55 AM
easyData ScientistOnsiteStatistics & Math
28
0

Assess Probability of Heads in Coin Tosses

Probability with Coin Tosses and the Normal Distribution

Context

Onsite data scientist screening question assessing basic probability and distribution knowledge.

Questions

  1. A fair coin is tossed N times, with independent tosses. What is the probability of observing exactly k heads?
  2. How does your answer change if the coin is biased, with probability p of heads on each toss?
  3. Let X ~ N(μ, σ²). Derive P(a < X < b) and explain how to standardize a normal variable.

Hint

  • Use the binomial probability mass function (pmf) for parts (1) and (2).
  • Use the Z-score transformation to standardize a normal variable.

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?
Loading comments...

Browse More Questions

More Statistics & Math•More Upstart•More Data Scientist•Upstart Data Scientist•Upstart Statistics & Math•Data Scientist Statistics & Math