# Example 8 - Chapter 13 Class 12 Probability

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

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) = 1015 = 23 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 𝑏𝑎𝑙𝑙𝑟𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔 𝑏𝑎𝑙𝑙𝑠 = 914 Now, P(E ∩ F) = P(E) P(F|E) . = 23 × 914 = 𝟑𝟕

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Chapter 13 Class 12 Probability

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.