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TS EAMCET · Maths · Probability

A candidate takes three tests in succession and the probability of passing the first test is \(p\). The probability of passing each succeeding test is \(p\) or \(\frac{p}{2}\) according as he passes or fails in the preceding one. The candidate is selected, if he passes atleast two tests. The probability that the candidate is selected, is

  1. A \(p^2(2-p)\)
  2. B \(p(2-p)\)
  3. C \(p+p^2+p^3\)
  4. D \(p^2(1-p)\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(p^2(2-p)\)

Step-by-step Solution

Detailed explanation

Required probability \(=\) Probability of passing two test + Probability of passing all three test \(=P\) (passing \(\mathrm{I}\) and \(\mathrm{II}\) tests and fail in third test) \(+P\) (passing Ist test, fail in II test and passing in IIIrd test) + \(P\) (fail in I test,…