Question
Two dice are rolled, write the sample space ‘S’ and number of sample points
n(S). Also write events and number of sample points in the event according to the
given condition.
(i) Sum of the digits on upper face is a prime number.
(ii) Sum of the digits on the upper face is multiple of 5.
(iii) Sum of the digits on the upper face is 25.
(iv) Digit on the upper face of the first die is less than the digit on the second die.

Answer

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)} n(S)=36
(i) Event (E) : The sum of the digits on the upper face is a prime number.
E = {(1,1),(1,2),(1,4),(1,6),(2,1),(2,3),(2,5),(3,2),(3,4),
(4,1),(4,3),(5,2),(5,6),(6,1),(6,5)}
(\therefore) n ( E )=15
(ii) Event (F) : The sum of the digits on the upper face is a multiple of 5.
(F ={(1,4),(2,3),(3,2),(4,1),(4,6),(5,5),(6,4)}
(\therefore) n ( F )=7)
(iii) Event (G) : The sum of the digits on the upper face is 25 .
G ={}=(\phi)
(\therefore) n ( G )=0
(iv) Event (H) : The number on upper face of first die is less than the digit on second die.
H ={(1,2)(1,3)(1,4)(1,5)(1,6)(2,3)(2,4)(2,5)(2,6)
(3,4)(3,5)(3,6)(4,5)(4,6)(5,6)}
(\therefore) n ( H )=15

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