Two fair dice are rolled. Let `P(A_(i))gt0` donete the event that the sum of the faces of the dice is divisible by i. For which one of the following (

Question

Two fair dice are rolled. Let `P(A_(i))gt0` donete the event that the sum of the faces of the dice is divisible by i. For which one of the following (

Two fair dice are rolled. Let `P(A_(i))gt0` donete the event that the sum of the faces of the dice is divisible by i.
For which one of the following (I,j) are the events `A_(i)and A_(j)` independent ?
A. `(3,4)`
B. `(4,6)`
C. `(2,3)`
D. `(4,2)`

Monjur Alahi

7 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 - C
`P(A_(2))=1/2,P(A_(3))=1/3,P(A_(6))=1/6`
`thereforeP(A_(2)nnA_(3))=P(A_(2))P(A_(3))`
`impliesP(A_(6))=P(A_(2))P(A_(3))`
`6/36=1/2xx1/3`
Hence, `A_(2)and A_(3)` are independent.

7 views Answered 2023-02-05 15:29