GMAT Focus EditionQuantitative ReasoningEasy
A quality control inspector monitors a production line where widgets are manufactured. The probability that a randomly selected widget is defective is 0.02. If the inspector randomly selects 100 widgets, what is the expected number of defective widgets in the sample?
- A5
- B1
- C10
- D2
Show answer & explanationAnswer & explanation
Correct answer: D. 2
The expected number of events in a series of trials is calculated by multiplying the number of trials by the probability of the event occurring in a single trial. In this case, 100 widgets multiplied by a 0.02 probability of defect gives 2 expected defective widgets.
Why the other options are wrong
- A. This would be the expected number if the probability was 0.05.
- B. This would be the expected number if the probability was 0.01.
- C. This would be the expected number if the probability was 0.10.
Expected Value (Discrete Random Variable)
For a discrete random variable representing the number of successes in 'n' trials, where the probability of success in a single trial is 'p', the expected value (mean) is E(X) = np.
- Represents the average outcome over many trials.
- Not necessarily an outcome that will occur on any single trial.
- Used in probability and statistics for predictions.
Memory trick: Expect N-P to Predict Outcomes.