Statistics

How can you tell if a given coin is biased?

Data Scientist

Google

Takeaway

Blind

Medallia

PagerDuty

MongoDB

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Answers

Anonymous

6 months ago
4Strong
Determining if a coin is biased involves testing whether the coin lands on heads or tails with equal probability. Here's a step-by-step approach to figure out if a coin is biased:

1. Formulate a Hypothesis

  • Null Hypothesis (H0): The coin is fair (i.e., the probability of landing heads is 0.5).
  • Alternative Hypothesis (H1): The coin is biased (i.e., the probability of landing heads is not 0.5).

2. Conduct a Series of Trials

  • Flip the coin a large number of times (e.g., 100, 200, or more). The more trials, the more reliable your results.
  • Record the outcome of each flip (heads or tails).

3. Calculate the Proportion of Heads

  • Count the number of heads HH and the total number of flips NN.
  • Calculate the proportion of heads: p=Number of Heads / Total number of flips
4.Calculate the Z-Score:
  • The Z-score measures how many standard deviations the observed proportion is from the expected proportion.
compate the z score aginst the established confidence level established and pvalue to determine if we can reject the null hypothosis or not

  • Is there a specific method you use to detect if a coin is unevenly weighted?
  • In your opinion, what are the telltale signs of an imbalanced coin?
  • Can you walk me through the process of determining the bias of a coin?
  • How would you differentiate between a fair coin and one that has a bias?
  • Have you ever encountered a coin that you suspected to be biased? If so, what gave it away?
  • What factors do you consider when assessing the fairness of a coin?
  • Is there a way to confirm if a coin is biased without testing it in a large sample size?
  • What warning signs do you observe when examining a coin for bias?
  • Do you believe there are any innate properties of a coin that might make it more susceptible to bias?
  • What indications would you look for to identify a potentially biased coin?
  • How can you tell if a given coin is biased?
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Interview question asked to Data Scientists interviewing at Akamai, Shopee, Google and others: How can you tell if a given coin is biased?.