If two dice are thrown and at least one of the dice shows 5, then the probability that the sum is 10 or more is

Step-by-step solution

aligned & A = Event of showing 5 and atleast one dice & =(1,5),(2,5),(3,5),(4,5)(5,5),(6,5),(5,1) , & (5,2),(5,3),(5,4),(5,6) & n( ~A )=11 & and n(s)=6 6=36 & B= Event of showing sum 10 or more when atleast one & dice shows 5 & =(5,5),(5,6),(6,5) & n( ~B )=3 & n( ~A ~B )=3 & Now, P ( ~B ~A )= P ( ~A ~B ) P ( ~A ) & = n( ~A ~B ) n( ~S ) n( ~A ) n( ~S ) = 3 36 11 36 = 3 11 aligned