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Example 8 - An urn contains 10 black, 5 white balls. Two balls - Multiplication rule of probability

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  1. Chapter 13 Class 12 Probability
  2. Serial order wise
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Example 8 An urn contains 10 black and 5 white balls. Two balls are drawn from the urn one after the other without replacement. What is the probability that both drawn balls are black? We need to find probability that both balls drawn out are black Let the events be E : First ball drawn is black F : Second ball drawn is black Probability both balls drawn are black = Probability first ball drawn is black × Probability second ball is black if first is black P(E ∩ F) = P(E) P(F|E) P(E) is Probability first ball drawn is black There are 10 blacks balls out of 15 So, P(E) = 10﷮15﷯ = 2﷮3﷯ P(F|E) is the Probability of F after E has happened i.e. probability of second ball drawn black if first ball was black If first ball drawn was black, we are left with 9 black, 5 white balls P(F|E) = 𝑅𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔 𝐵𝑙𝑎𝑐𝑘 𝑏𝑎𝑙𝑙﷮𝑟𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔 𝑏𝑎𝑙𝑙𝑠﷯ = 9﷮14﷯ Now, P(E ∩ F) = P(E) P(F|E) . = 2﷮3﷯ × 9﷮14﷯ = 𝟑﷮𝟕﷯

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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