APFIVE Conditional Probability and Independence
The probability that a randomly selected student uses a guessing strategy is $$0.3$$. Among students who score below 60, the probability of using a guessing strategy is $$0.25$$. Are the events “using a guessing strategy” and “scoring below 60” independent?
A
Yes, because any deviation is due to random chance.
B
The events are complementary, not independent.
C
They would be independent if $$P(<60|Guess) = P(<60)$$, but that is not given.
D
No, because independence requires $$P(Guess|<60) = P(Guess)$$ and here $$0.25 \neq 0.3$$.
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