## Since the fair coin has $1$ marked on one face and $6$ on the other and the die has six

faces that are numbered $1,2,3,4,5$ and $6$ the sample space is given by

$S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}$

$⇒n(S)=12$

(i) Let $A$ be the event in which the sum of numbers that turn up is $3$

$⇒A={(1,2)}$

$∴P(A)=TotalnumberofpossibleoutcomesNumberofoutcomesfavourabletoA =n(S)n(A) =121 $

(ii) Let $B$ be the event in which the sum of numbers that turn up is $12$

$⇒B={(6,6)}$

$∴P(B)=TotalnumberofpossibleoutcomesNumberofoutcomesfavourabletoB =n(S)n(B) =121 $