pa1 pb2 a and b are disjoint find the following Pba Pa and n

p(a)-.1
p(b)-.2
a and b are disjoint

find the following

P(b/a)
P(a and not b)
P(b/ not a)
p(a or not b)

Solution

p(a)-.1 p(not a)=0.9
p(b)-.2 p(not b)=0.8
a and b are independent
if a and b are  independent then a and not b are independent, not a and b are independent

P(b/ not a )= P(b intersection not a)/P(not a) = 0.2*0.9/0.9 = 0.2
p(a or b)= P(a) + P(b) - P(a intersection b)= 0.1 + 0.2 - 0.1*0.2 = 0.28
p(not a or not b)= P(not a) + P(not b) - P(not a intersection not b)= 0.9 + 0.8 - 0.9*0.8 = 0.98
p(a and not b) = 0.1*0.8= 0.08