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From a lot of 10 bulbs, which includes 3 defectives, asample of 2 bulbs is drawn at random. Find the probability distribution ofthe number of defective bulbs. |
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Answer» let no of defective bulbs be `x` `x= 0,1,2` total ways`= .^10C_2` ways in 2 defective`= .^3C_2` ways of 1 defective`= .^3C_1.^7C_1` ways of zero defectives`=.^7C_2` `P(x=0) = (.^7C_2)/(.^10C_2) = ((7*6)/2)/((10*9)/2)` `= 7/15` `P(x=1) = (.^3C_1.^7C_1)/(.^10C_2) = (3*7)/((10*9)/2)` `=7/15` `P(x=2)= (.^3C_2)/(.^10C_2)= ((3*3)/2)/((10*9)/2) = 1/15` |
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