1. Events A and B are dependent, P (A) = 20%, P (BIA) = 25%. What is P (A and B) ?

2. If P (A) = 12%, P (B) = 48% and P (A or B) = 50%. What is P (A and B) ?

1. Given that e vents A and B are dependent, P (A) = 20%, P (BIA) = 25%. What is P (A and B) ?

P (BIA) = [P (A and B) ]/P (A)

it follows then that:

P (A and B) = P (A) * P (BIA)

P (A) = 0.2

P (BIA) = 0.25

hence

P (A and B) = 0.2*0.25=0.05=5%

2. Given that P (A) = 12%, P (B) = 48% and P (A or B) = 50%. What is P (A and B) ?

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

but

P (A) = 12%, P (B) = 48%, P (A and B) = 50%

thus

P (A or B) = 12%+48%-50%

simplifying the above we obtain:

P (A or B) = 60%-50%=10%