AP EAMCET · Maths · Probability
The probability that a student gets distinction in a Mathematics test is \(\frac{2}{3}\). If five such tests are conducted over a certain period of time, then the probability that he gets distinction in atleast 3 tests is
- A \(\frac{112}{243}\)
- B \(\frac{17}{81}\)
- C \(\frac{131}{243}\)
- D \(\frac{64}{81}\)
Answer & Solution
Correct Answer
(D) \(\frac{64}{81}\)
Step-by-step Solution
Detailed explanation
\(P(X=k) = C(n, k) p^k q^{n-k}\), where \(n=5\), \(p=\frac{2}{3}\), \(q=1-\frac{2}{3}=\frac{1}{3}\) \(P(X \ge 3) = P(X=3) + P(X=4) + P(X=5)\) \(P(X=3) = C(5, 3) (\frac{2}{3})^3 (\frac{1}{3})^2 = 10 \cdot \frac{8}{27} \cdot \frac{1}{9} = \frac{80}{243}\)…
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