If a box has 100 pens of which 10 are defective, then what is the probability that out of a sample of 5 pens drawn one by one with replacement atmost

Monjur Alahi

If a box has 100 pens of which 10 are defective, then what is the probability that out of a sample of 5 pens drawn one by one with replacement atmost one is defective?
A. `(9/10)^(5)`
B. `1/2(9/10)^(4)`
C. `1/2(9/10)^(4)`
D. `(9/10)^(5)+1/2(9/10)^(4)`


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Salim Ahmed Kawsar

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Here, n=5,p`=10/100=1/10andq=9/10`
`rle1`
`rArrr=0,1`
Also, `P(X=r)=""^(n)C_(r)p^(r )q^(n-r)`
`therefore P(X=r)=P(r=0)+P(r=1)`
`=""^(5)C_(0)(1/10)^(0)(9/10)^(4)`
`=(9/10)^(5)+5cdot1/10cdot(9/10)^(4)`
`(9/10)^(5)+1/2(9/10)^(4)`

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