AP EAMCET2014MathematicsProbability
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 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
Options
- Ap^2(2-p)
- Bp(2-p)
- Cp+p^2+p^3
- Dp^2(1-p)
Correct answer
A. p^2(2-p)
Step-by-step solution
Required probability = Probability of passing two test + Probability of passing all three test =P (passing I and 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, passing in IInd and IIIrd tests) +P (passing in all three tests) aligned & =n p q+p q p 2 +q p 2 p+p p p & =p^2(1-p)+p(1-p) p 2 +(1-p) p^2 2 +p^3 & =p^2 (1-p+ 1 2 - p 2 + 1 2 - p 2 +p )=p^2(2-p) aligned