In Example 1.4, we assumed all sides of the die are equally likely. The probabilities do not have to be equally likely. For instance, consider the foowing probabilities: Pr[1]=.5 Prlk] = {1.1 for l: = 2,3,4,5,6 Then, repeating the above calculations. Pr[A] = Pr[ {1,2,3,4}] (list the outcomes oils} = Pr[l] + Pr[2] + Pr[3] + Pr[4] (break the event into its outcomes} 1 l 1 1 8 . . . E + E + E + E E {unequal probahllioes) 3 Pr[B] = Pr[2,4,s] = E Continuing, A LIB = {1,2,3,4,}, and AB = {2,4}. Thus, Pr [A LIB] = Pr[ {1,2, 3, 4, 6}] = % (rst, solve directly} = P1121] + Pr[B] PrIAB] (second, solve 1with union formula] - E .,. i _ i - i _ is 10 to _ ID Alternatively. Pr[AuB] = 114.43] +Pr[A] +Pr[is] = 12!) + % + $ = %