KCET · Maths · Area Under Curves
A box contains \( 100 \) bulbs, out of which \( 10 \) are defective. A sample of \( 5 \) bulbs is drawn. The
probability that none is defective is
- A \( \left(\frac{1}{10}\right)^{5} \)
- B \( \left(\frac{1}{2}\right)^{5} \)
- C \( \frac{9}{10} \)
- D \( \left(\frac{9}{10}\right)^{5} \)
Answer & Solution
Correct Answer
(D) \( \left(\frac{9}{10}\right)^{5} \)
Step-by-step Solution
Detailed explanation
Given that, total number of bulbs are 100 .
Defective bulbs are 10 .
So, \(p=\frac{10}{100}=0.1, q=0.9, n=5\)
Therefore \(p(x)={ }^{5} C_{x}(p)^{x}(q)^{5-x}\)
\(p(0)={ }^{5} C_{0}(0.1)^{0}(0.9)^{5}\)
\(=\left(\frac{9}{10}\right)^{5}\)
Defective bulbs are 10 .
So, \(p=\frac{10}{100}=0.1, q=0.9, n=5\)
Therefore \(p(x)={ }^{5} C_{x}(p)^{x}(q)^{5-x}\)
\(p(0)={ }^{5} C_{0}(0.1)^{0}(0.9)^{5}\)
\(=\left(\frac{9}{10}\right)^{5}\)
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