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AP Statistics 4.4 Mutually Exclusive Events- MCQs - Exam Style Questions

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Question

When manufacturing a certain smartphone, defects occur at different rates depending on the type of defect. Specifically, screen-related defects occur in \(1\%\) of phones, defects related to the charging port occur in \(2\%\) of phones, and both defects occur in \(0.5\%\) of phones. What is the probability a phone has a screen-related defect, given that it has a defect related to the charging port?
(A) \(0.0300\)
(B) \(0.0302\)
(C) \(0.2000\)
(D) \(0.2500\)
(E) \(0.5000\)
▶️ Answer/Explanation
Detailed solution

1. Identify the Goal and Given Probabilities:
– We need to find the conditional probability \(P(\text{Screen defect} | \text{Charging defect})\).
– \(P(\text{Screen and Charging}) = 0.005\)
– \(P(\text{Charging}) = 0.02\)

2. Apply the Conditional Probability Formula:
\(P(A|B) = \frac{P(A \text{ and } B)}{P(B)}\)
\(P(\text{Screen} | \text{Charging}) = \frac{P(\text{Screen and Charging})}{P(\text{Charging})}\)

3. Calculate the Probability:
\(P(\text{Screen} | \text{Charging}) = \frac{0.005}{0.02} = 0.25\)
✅ Answer: (D)

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