Suppose that A and B are two events for which P()=0.18P(A)=0.18, P()=0.78P(B)=0.78, and P(|)=0.48P(B|A)=0.48 Find each of the following, accurate to 4 decimal places: A. P(and)=P(A and B)= B. P(or)=P(A B)= C. P(|)=P(A|B)=

(a)  P(A and B) =0.0864

(b) P(A or B)= 0.8736

(c) P(A|B) =0.1108

Step-by-step explanation:

Probability: The ratio of the favorable outcome to the the total outcomes.

P(A∩B) means the common element of A and B event.

P(A∪B) means all element of A and B event.

Conditional probability:A probability of a event occurring with some presents another event .

Given, P(A) = 0.18 , P(B)=0.78  and P(B|A)=0.48

We know that,

(a)

If two event are independents means the outcome of one event does not affect the outcome of other.

Then P(A and B)= P(A)× P(B)

If two event are dependent means the outcome of one event affects the outcome of other.

Then P(A and B)= P(A)P(B|A)

Since here A and B dependent .

Then P(A and B)= P(A∩B)

P(A and B)= 0.0864

(b)

If two events are mutually exclusive.

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

If two events are non mutually exclusive.

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

Therefore

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

⇒ P(A or B)= 0.18+0.78-0.0864

⇒P(A or B)= 0.8736

(c)

                =0.11076

                ≈ 0.1108

it's