Can some solve for me step by step with explanation on how t

Can some solve for me step by step with explanation on how to get the answer. I am very weak in statistics and have no background. Deeply appreciated. Thanks

6. Show that: a. If A and B are mutually exclusive events, and if Pr(A)F.5, and Pr(A or B).6, then If A and B are mutually exclusive events, and if Pr(A).5, and Pr(A or B-6, then a. b. If A and B are independent, then Pr(A or B) = 1 -Pr(not A)Pr(not B)

Solution

a)For a mutually exclusive event

Pr(A or B)=Pr(A)+Pr(B)

Given ,Pr(A)=.5 and P(A or B)=.6

Substitute to find P(B)

.5+P(B)=.6

P(B)=.1 -------->proved

b)P(A or B)=P(A)+P(B)-P(A and B)

For and independent event P(A and B)=P(A)*P(B)

                 =P(A)+P(B)-P(A)P(B)

         =1-P(A\')+1-P(B\')-[1-P(A\')][1-P(B\')]

           =2-P(A\')-P(B\')-(1-P(B\')-P(A\')+P(A\')P(B\')

            =1-P(A\')P(B\') ----------->PROVED