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AP EAMCET · Maths · Probability

\(U_1, U_2, U_3\) are three urns. \(U_1\) contains 5 red, 3 white, 2 back balls; \(U_2\) contains 4 red, 4 white, 2 black balls and \(U_3\) contains 3 red, 4 white, 3 black balls. If a ball is chosen at random from an urn chosen at random, then the probability of not getting a black ball is

  1. A \(\frac{7}{30}\)
  2. B \(\frac{23}{30}\)
  3. C \(\frac{2}{5}\)
  4. D \(\frac{11}{30}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(\frac{23}{30}\)

Step-by-step Solution

Detailed explanation

\(P(U_i) = \frac{1}{3}\) \(P(NB|U_1) = \frac{5+3}{10} = \frac{8}{10}\) \(P(NB|U_2) = \frac{4+4}{10} = \frac{8}{10}\) \(P(NB|U_3) = \frac{3+4}{10} = \frac{7}{10}\) \(P(NB) = P(U_1)P(NB|U_1) + P(U_2)P(NB|U_2) + P(U_3)P(NB|U_3)\)…