Statistics And Probability Question 578
Question: A sample of 4 items is drawn at a random without replacement from a lot of 10 items. Containing 3 defective. If X denotes the number of defective items in the sample then $ P(0<x<3) $ is equal to
[J & K 2005]
Options:
A) $ \frac{3}{10} $
B) $ \frac{4}{5} $
C) $ \frac{1}{2} $
D) $ \frac{1}{6} $
Show Answer
Answer:
Correct Answer: B
Solution:
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Since the item are choosen without replacement. \ $ P(X=x)=\frac{^{3}C_{x}{{+}^{7}}{C_{4-x}}}{^{10}C_4} $ Putting $ x=1,\,2 $ we have $ P(0<x<3) $ $ =\frac{^{3}C_1{{\times }^{7}}C_3}{210}+\frac{^{3}C_2{{\times }^{7}}C_2}{210} $ $ =\frac{3\times 35+3\times 21}{210}=\frac{105+63}{210}=\frac{168}{210}=\frac{4}{5} $ .
BETA
