Probability
Binomial Distribution
Grade 12
Question:
<p>The probability that a computer is defective is \(\dfrac{1}{500}\). Computers are packed in boxes of 10. Which of the following about \(P(\text{no defective in a box})\) are TRUE?</p>
The probability that a box has no defective computer is 1 - (1/500)^10.
The probability that a box has no defective computer is 1 - 10*(1/500).
The probability that a box has no defective computer is 1 - 9*(1/500).
The probability that a box has no defective computer is 1 - (1/500)^5.
Step-by-Step Solution
Key Concept: X ~ Bin(10, 1/500). All four statements follow directly from the binomial distribution.
<p>$P(X=0)=\left(\frac{499}{500}\right)^{10}\approx (0.998)^{10}\approx 0.9802$. <strong>A✓, B✓</strong>.</p><p>$P(X\geq1)=1-P(X=0)$. <strong>C✓</strong>.</p><p>$P(X=1)=\binom{10}{1}(\frac{1}{500})(\frac{499}{500})^9$. <strong>D✓</strong>.</p>
Correct Answer: ABCD