1.

Two dice are rolled simultaneously. Event A : The sum of the digits on the upper face is a multiple of 6. Event B : The sum of the digits on the upper face is minimum 10. Event C : The same digit on both the upper faces.

Answer» Two dice are rolled simultaneously.
`therefore` the sample space
S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}
`thereforen(S)=36.`
Event A : The sum of the digits on upper face is a multiple of 6.
`thereforeA={(1,5),(2,4),(3,3),(4,2),(5,1),(6,6)}.`
`thereforen(A)=6.`
Event B : The sum of the digits on upper face is minimum 10.
`therefore B={(4,6),(5,5),(5,6),(6,4),(6,5),(6,6)}.`
`thereforen(B)=6.`
Event C : The same digit on both the upper faces.
`thereforeC={(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)}.`
`thereforen(C)=6.`


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