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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.
Define the Events:
Given Probabilities:
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(G∣C)⋅P(C)+P(G∣L)⋅P(L)
Plugging in the given values:
P(G)=0.6⋅0.8+1⋅0.2
Simplify:
P(G)=0.48+0.2=0.68
Conclusion: Therefore, the probability that a randomly selected movie is rated as "good" is 0.68, or 68%.
Understanding the Problem:
Use of Conditional Probability:
Law of Total Probability:
By understanding these principles and applying them correctly, we can confidently determine the probability of a movie being rated "good" in this scenario.