Question

10 + 5 Points!

Two dice are rolled. What is the probability that the sum of the numbers rolled is
a) not less than 7?
b) not more than 7?

Answer 1

`P(A)=(|A|)/(|\Omega|)\\\\ |\Omega|={6+2-1\choose 2}={7\choose 2}=(7!)/(2!5!)=(6\cdot7)/(2)=21\\\\ a)\\ A=\{(1,6),(2,6),(3,6),(4,6),(5,6),(6,6),(2,5),(3,5),(4,5),(5,5),\\ (3,4),(4,4)\}\\ |A|=12\\ P(A)=(12)/(21)=(4)/(7)\\\\ b)\\ A=\{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,2),(2,3),(2,4),(2,5),\\ (3,3),(3,4)\}\\ |A|=12\\ P(A)=(12)/(21)=(4)/(7)`