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: This question evaluates understanding of discrete and continuous probability concepts, specifically the binomial model for repeated Bernoulli trials and the normal distribution with standardization, testing core statistical reasoning and sensitivity to distribution parameters.