InterviewSolution
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InterviewSolution
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Four persons are to be chosen at random from a group of 3 men, 2 womenand 4 children. Find the probability of selecting:(i)1man 1woman and 2 children(ii)Exactly 2 children (iii) 2 women |
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Answer» Total persons=2+3+4=9 total ways=`.^9C_4` 1)`.^3C_!*.^2C_1*.^4C_2` favorable cases `P=(.^3C_1*.^2C_1.^4C_1)/(.^9C_4)` `P=2/7` 2)Exactly 2 children Case 1) 2 childdren 1 men 1 women `.^4C_2*.^3C_1*.^2C_1` Case 2) 2 children 2 mean 0 women `.^4C_2*.^3C_2` Case 3) 2 children 0 mean 2 women `.^4C_2*.^2C_2` Total ways=`.^4C_2*.^3C_1*.^2C_1+.^4C_2.^3C_2+.^4C_2.^2C_2` `=10/21` Case1)`.^2C_2*.^4C_1*.^3C_1=1*4*3=12` Case2)`.^2C_2*.^4C_2=6` Case3)`.^2C_2*.^3C_2=1*3=3` `P=(12+6+3)/(.^9C_4)=1/6`. |
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