Question

For two events A A and B B , P(A)=0.2 P(A)=0.2 and P(B)=0.4 P(B)=0.4 . (a) If A A and B B are independent, then P(A|B) P(A|B) = = equation editor Equation Editor P(A∩B) P(A∩B) = = equation editor Equation Editor P(A∪B) P(A∪B) = = equation editor Equation Editor (b) If A A and B B are dependent and P(A|B)=0.1 P(A|B)=0.1 , then P(B|A) P(B|A) = = equation editor Equation Editor P(A∩B) P(A∩B) = = equation editor Equation Editor

Answer 1

p(A) = 0.2, P(B) = 0.4

a)

If A nad B are independent, then P(A B) = P(A) * P(B)

So,

P(A | B) = P(A B) / P(B)

= P(A) * P(B) / P(B)

= P(A)

= 0.2

P(A | B) = 0.2

P(A B) = P(A) * P(B)

= 0.2 * 0.4

= 0.08

P(A B) = 0.08

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

= 0.2 + 0.4 - 0.08

= 0.52

P(A B) = 0.52

b)

Given, A and B are dependent.

P(A |B) = 0.1

First calculate P(A B) = ?

P( A | B) = P(A B) / P(B)

0.1 = P(A B) / 0.4

P(A B) = 0.1 * 0.4

P(A B) = 0.04

Therefore,

P(B | A) = P(A B) / P(A)

= 0.04 / 0.2

= 0.2

P(B | A) = 0.2