1. A plane is ruled with parallel straight lines at equal distances of 2a. A needle, 2L long(L

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2. A lot contains 20 articles.The probablility that the lot contains exactly 2 defective articles is 0.4 and that the lot contains exactly 3 defective articles is 0.6 . Articles are drawn from the lot at random one by one without replacement and are tested till all the defective articles are found. What is the probability that the testing procedure ends at th 12th testing.

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Dear Sudip

let

A=testing procedure ends at 12th testing

A1 =lot contain 2 defective article

A2 =lot contain 3 defective article

required probability=P(A)

                            =P(A∩ A1)∩ (A∩A2)

                            =P(A∩ A1)+(A∩A2)

                           =P(A1)P(A/A1)  + P(A2)P(A/A2)

 

now  P(A/A1)=probability that first 11 draws contain 10 non defective and 1 defective and 12th draw contain a defective article

                 =¹⁸C₁₀ X²C₁/²⁰C₁₁  X  1/9

 

 and P(A/A1)=probability that first 11 draws contain 9  non defective and 2 defective and 12th draw contain a defective article

                 =¹⁷C₉ X³C2/²⁰C₁₁  X  1/9

Hence required probability

    = 0.4 X ¹⁸C₁₀ X²C₁/²⁰C₁₁  X  1/9        +0.6 X ¹⁷C₉ X³C2/²⁰C₁₁  X  1/9

 

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