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Data Interview Question

Movie Rating Probability

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Solution & Explanation

To solve this problem, we need to determine the probability that a randomly selected movie is rated as "good" by the evaluators at Netflix. We have two types of raters: diligent raters and lazy raters.

Step-by-Step Breakdown:

  1. Define the Events:

    • Let GG be the event that a movie is rated as "good."
    • Let CC be the event that a rater is diligent (careful).
    • Let LL be the event that a rater is lazy.
  2. Given Probabilities:

    • P(GC)=0.6P(G|C) = 0.6: The probability that a movie is rated as "good" given that the rater is diligent.
    • P(GL)=1P(G|L) = 1: The probability that a movie is rated as "good" given that the rater is lazy.
    • P(C)=0.8P(C) = 0.8: The probability that a rater is diligent.
    • P(L)=0.2P(L) = 0.2: The probability that a rater is lazy.
  3. Apply the Law of Total Probability: The probability that a movie is rated as "good" can be found by considering both types of raters:

    P(G)=P(GC)P(C)+P(GL)P(L)P(G) = P(G|C) \cdot P(C) + P(G|L) \cdot P(L)

    Plugging in the given values:

    P(G)=0.60.8+10.2P(G) = 0.6 \cdot 0.8 + 1 \cdot 0.2

    Simplify:

    P(G)=0.48+0.2=0.68P(G) = 0.48 + 0.2 = 0.68

  4. Conclusion: Therefore, the probability that a randomly selected movie is rated as "good" is 0.68, or 68%.

Explanation

  • Understanding the Problem:

    • We have two types of raters with different behaviors. Diligent raters have a mixed rating pattern (60% good, 40% bad), while lazy raters always rate a movie as "good."
    • The challenge is to combine these behaviors to find the overall probability of a movie being rated "good."
  • Use of Conditional Probability:

    • The problem involves conditional probabilities because the rating depends on the type of rater.
    • Conditional probability helps us determine the likelihood of an event occurring given another event has occurred.
  • Law of Total Probability:

    • This law allows us to calculate the probability of an event by considering all possible ways the event can occur, weighted by the probability of each way.
    • Here, it helps us combine the probabilities from both diligent and lazy raters.

By understanding these principles and applying them correctly, we can confidently determine the probability of a movie being rated "good" in this scenario.