TS EAMCET · Maths · Probability
Among every 8 units of a product, one is likely to be defective. If a consumer has ordered 5 units of that product, then the probability that atmost one unit is defective among them is
- A \(\frac{15}{8}\left(\frac{7}{8}\right)^6\)
- B \(\frac{57}{8^8}\)
- C \(\frac{36}{8^5}\)
- D \(\frac{3}{2}\left(\frac{7}{8}\right)^4\)
Answer & Solution
Correct Answer
(D) \(\frac{3}{2}\left(\frac{7}{8}\right)^4\)
Step-by-step Solution
Detailed explanation
\(P(\text{defective}) = p = \frac{1}{8}\) \(P(\text{non-defective}) = q = 1 - p = \frac{7}{8}\) \(P(X=k) = C(n, k) p^k q^{n-k}\) \(P(X \le 1) = P(X=0) + P(X=1)\) \(P(X=0) = C(5, 0) \left(\frac{1}{8}\right)^0 \left(\frac{7}{8}\right)^5 = \left(\frac{7}{8}\right)^5\)…
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