Let two fari six-faced dice A and B be thrown simltaneously. If `E_(1)` is the event that die A shows up four, `E_(2)` is the event that die B shows u

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Let two fari six-faced dice A and B be thrown simltaneously. If `E_(1)` is the event that die A shows up four, `E_(2)` is the event that die B shows up two and `E_(3)` is the event that the sum of numbers on both dice isodd, then which of the following statement is NOT True ?
A. `E_(2)and E_(3)` are independent
B. `E_(1)and E_(3)` are independent
C. `E_(1)and E_(2) and E_(3)` are independent
D. `E_(1)and E_(2)` are independent


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Salim Ahmed Kawsar

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Correct Answer - C
`E_(1):{(4,1),...,(4,6)}to6"cases"`
`E_(2):{(1,2),...,(6,2)}to6"cases"`
`E_(3):"18 cases (sum of both is odd")`
`thereforeP(E_(1))=3/6=1/6=P(E_(2))`
`P(E_(3))=18/36=1/2`
`P(E_(1)nnE_(2))=1/36`
`P(E_(2)nnE_(3))=3/36=1/12`
Similarly `P(E_(3)nnE_(1))=1/12`
`P(E_(1)nnE_(2)nnE_(3))=0`
`therefore E_(1),E_(2),E_(3)` are not independent.

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