Paragraph: A fair die is tossed repeatedly until a six is obtained. Let X denotes the number of tosses required. Question: The conditional probability that X ≥ 6 given X 3 equals

Question

Paragraph: A fair die is tossed repeatedly until a six is obtained. Let X denotes the number of tosses required. Question: The conditional probability that X ≥ 6 given X > 3 equals

TestHub · Accepted Answer

P (( X ≥ 6 ) / ( X > 3 )) ​ = P ( X > 3 ) P (( X > 3 ) / ( X ≥ 6 )) ⋅ P ( X ≥ 6 ) ​ = [ ( 6 5 ​ ) 3 ⋅ 6 1 ​ + ( 6 5 ​ ) 4 ⋅ 6 1 ​ + … ∞ ] 1 ⋅ [ ( 6 5 ​ ) 5 ⋅ 6 1 ​ + ( 6 5 ​ ) 6 ⋅ 6 1 ​ + … ∞ ] ​ = 36 25 ​ ​

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