If AA and BB are two disjoint events with P (A) = 0.15P (A) = 0.15 and P (B) = 0.75P (B) = 0.75, find the following probabilities:

a) P (A and B) = P (A and B) =

b) P (A or B) = P (A or B) =

c) P (not A) = P (not A) =

d) P (not B) = P (not B) =

e) P (not (A or B)) = P (not (A or B)) =

f) P (A and (not B)) = P (A and (not B)) =

a 0

b) 0.9

c) 0.85

d) 0.25

e) 0.1

f) 0.0375

Step-by-step explanation:

a)

As A and B are two disjoints events, then P (A and B) is

P (A and B) = 0

b)

As A and B are two disjoints events, then P (A or B) is

P (A or B) = P (A) + P (B)

P (A or B) = 0.15+0.75=0.9

c)

P (not A) = 1-P (A)

P (not A) = 1-0.15=0.85

d)

P (not B) = 1-P (B)

P (not B) = 1-0.75=0.25

e)

P (not (A or B)) = 1-P (A or B)

P (not (A or B)) = 1-0.9=0.1

f)

P (A and (not B)) = P (A) * P (not B)

P (A and (not B)) = 0.15*0.25=0.0375