PROBLEM 3E

Let A and B be independent events with P(A) = 1/4 and P(B) = 2/3. Compute (a) P(A∩B), (b) P(A∩B' ),

(c) P(A' ∩ B' ), (d) P[(A ∪ B) ' ], and (e) P(A' ∩ B).

Solution 3E

Step1 of 3:

We have the events A and B are independent events.

P(A) = and

P(B) =

We need to find,

(a) P(A∩B), (b) P(A∩B' ),

(c) P(A' ∩ B' ), (d) P[(A ∪ B) ' ],

(e) P(A' ∩ B).

Step2 of 3:

a).

Consider,

P(AB) = P(A)P(B) [because we know that A and B are independent]

=

=

=

Therefore, P(AB) = .

b).

Consider,

P(A∩B' ) = P(A)P(B1) [because we know that A and B are independent]

= [1-]

=

=

Therefore, P(A∩B' ) = .

c).

Consider,

P(A' ∩ B' ) = P(A1)P(B1) [because we know that A and B are independent]

= [1-] [1-]

=

...