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

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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