Probability
Classical Probability
Grade 12
Question:
<p>There are 4 defective items in a lot of 10 items. If 5 items are selected at random, the probability that the selected items contain at most 1 defective item is</p>
<p>\(\dfrac{5}{21}\)</p>
<p>\(\dfrac{7}{21}\)</p>
<p>\(\dfrac{11}{42}\)</p>
<p>\(\dfrac{1}{6}\)</p>
Step-by-Step Solution
Key Concept: At most 1 defective = 0 defective + exactly 1 defective. Use hypergeometric counting.
<p>Total: $\binom{10}{5} = 252$.</p><p>$P(0\text{ defective}) = \dfrac{\binom{4}{0}\binom{6}{5}}{252} = \dfrac{6}{252}$</p><p>$P(1\text{ defective}) = \dfrac{\binom{4}{1}\binom{6}{4}}{252} = \dfrac{4 \times 15}{252} = \dfrac{60}{252}$</p><p>$P(\leq 1) = \dfrac{6 + 60}{252} = \dfrac{66}{252} = \dfrac{11}{42}$</p>
Correct Answer: C