Praxis Core Academic Skills for Educators: Mathematics (5733)Statistics and ProbabilityMedium
A quality control manager is inspecting a batch of 100 manufactured parts. The manager finds that 8 parts are defective. If the manager randomly selects 2 parts from the batch for further testing, without replacement, what is the probability that both selected parts are defective?
- A0.0057
- B0.0064
- C0.0067
- D0.0056
Show answer & explanationAnswer & explanation
Correct answer: D. 0.0056
This is a problem involving dependent probability because the selections are without replacement. The probability of the first part being defective is 8/100. Given the first was defective, the probability of the second being defective is 7/99. Multiply these probabilities.
Why the other options are wrong
- A. This value is slightly off due to incorrect rounding or calculation.
- B. This would be the probability if the events were independent (8/100 * 8/100).
- C. This value is slightly off due to incorrect rounding or calculation.
Dependent Probability
The probability of two or more events occurring where the outcome of one event affects the outcome of the subsequent events.
- Events are 'without replacement'.
- The sample space changes after each event.
- Calculated by multiplying conditional probabilities.
Memory trick: Dependent means the next choice depends on the last.