Let two fair six-faced dice A and B be thrown simultaneously. 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 is odd, then whic h of the following statements is NOT True ?
Text Solution
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Sol. E 1 : {(4, 1) ,............... (4,6,)} 6 cases
E 2 : {(1,2), ............... (6,2)} 6 cases
E 3 : 18 cases (sum of both are odd)}
P(E 1 ) = 
= 
= P (E 2 )
P(E 3 ) = 
= 
P (E 1 ∩ E 2 ) = 
P(E 2 ∩ E 3 ) = 
P(E 3 ∩ E 1 ) = 
P(E 1 ∩ E 2 ∩ E 3 ) = 0
∴ E 1 , E 2 , E 3 are not independent
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