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
- A \(\frac{7}{30}\)
- B \(\frac{23}{30}\)
- C \(\frac{2}{5}\)
- D \(\frac{11}{30}\)
Answer & Solution
Correct Answer
(B) \(\frac{23}{30}\)
Step-by-step Solution
Detailed explanation
\(P(U_i) = \frac{1}{3}\) \(P(NB|U_1) = \frac{5+3}{10} = \frac{8}{10}\) \(P(NB|U_2) = \frac{4+4}{10} = \frac{8}{10}\) \(P(NB|U_3) = \frac{3+4}{10} = \frac{7}{10}\) \(P(NB) = P(U_1)P(NB|U_1) + P(U_2)P(NB|U_2) + P(U_3)P(NB|U_3)\)…
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