Quantitative Aptitude - Probability

41. What would be the expectation of the number of failures preceding the first success in an infinite series of independent trials with the constant probability of success p ?

  • Option : C
  • Explanation : Expectation of X = E(X) = average = mean

    Probability

    where pi denote probability of occurrence of xi
    Let q = 1-p
    Then probabilities of succession 1st, 2nd, 3rd 
    trials are
                       p, qp, q2p,......

    Probability

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42. A restaurant serves two special dishes A and B to its customers consisting of 60% men and 40% women. 80% of men order dish A and the rest B and 70% women order dish A and the rest B. In what ratio of A to B should the restaurant prepare the dishes?

  • Option : A
  • Explanation : Ratio of A and B = 60 x 80 + 40 x 70 : 60 x 20
    +40 x 30

    = 76 : 24
    = 19: 6

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43. If A and B are mutually exclusive and
P (A ∪ B) = P (A) + P (B), then
P(A/A ∪ B) =

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44. If P(A) = 0, then

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45. The mean of a set of number is x'. If each number is increased by λ, then mean of the new set is

  • Option : B
  • Explanation : "When each item is increased by λ, then mean is also increased by λ"
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