A box has 10 components, 2 of which are defective. If 2 are selected at random, what is the probability that at least one is defective?
Answer and explanation
Correct answer: A. 17/45
- Step 1: Use complement rule: P(at least 1 defective) = 1 - P(none defective).
- Step 2: Number of non-defective components: 8.
- Step 3: Ways to choose 2 non-defective: C(8, 2) = (8 * 7) / 2 = 28.
- Step 4: Total ways to choose 2 components: C(10, 2) = (10 * 9) / 2 = 45.
- Step 5: P(none defective) = 28 / 45.
- Step 6: P(at least 1 defective) = 1 - 28/45 = 17 / 45.
Answer
17/45.
Why not the others: '28/45' is the probability that none are defective; '1/5' (2/10) evaluates selecting 1 defective out of 10; '1/45' is the probability that both selected are defective.
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