Two fair dice,one red and one blue,are thrown.For each die:the possible scores are 1,2,3,4,5,6.Each score is equally likely,so each score has probability 1/6.You may assume that the score on reddie is independent of the score on the blue die.We define the following events.A:the sum of the scores on the dice is 7.B:the score on the red die is different from the score on the blue die.C:the sum of the scores on the dice is 11.D:the score on the red die is 6.0a.Calculate P(A).P(B).P(C)and P(D).b.Calculate P(A and B).P(A and C)and P(A and D).c.Calculate P(A or B).P(A or C)and P(A or D).d.Calculate P(B I A).P(C I A)and P(D I A).2Which of the following pairs of events are independent and why?a.A and B.b.A and C.c.A and D.3Now let E be the event that at least one 6 is thrown and F the event that two 6s are thrown.Calculatea.P(F I D).b.P(F IE).
