A fair die is tossed repeatedly until a 6 is obtained. Let X denote the number of tosses rerquired. The conditional probability that `Xge6` given `Xgt

Question

A fair die is tossed repeatedly until a 6 is obtained. Let X denote the number of tosses rerquired. The conditional probability that `Xge6` given `Xgt

A fair die is tossed repeatedly until a 6 is obtained. Let X denote the number of tosses rerquired.
The conditional probability that `Xge6` given `Xgt3` equals
A. `125//216`
B. `25//36`
C. `5//36`
D. `25//216`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - D
For `Xge6,` the probability is
`(5^(5))/(6^(6))+(5^(5))/(6^(7))+...oo=(5^(5))/(6^(6))((1)/(1-5//6))=((5)/(6))^(5)`
For `Xgt3,`
`(5^(3))/(6^(4))+(5^(4))/(6^(5))+(5^(5))/(6^(6))+...oo=((5)/(6))^(3)`
Hence, the conditional probability is
`((5//6)^(6))/((5//6)^(3))=25/36`

5 views Answered 2023-02-05 15:29