Question

12:34 X Statistics Test lesson 8-14... 7 U 2). Given the two way table, answer each question. X Y z A 20 10 40 B 10 15 20 C 30 25 10 P(A)= P(X)= P(A/B) = P(A/X)= 3). Using the two way table in question #2, find A). Two events that are independent B) Two mutually exclusive events C) Support your answers to A and B.

Answer 1

	A	B	C	Total
X	20	10	30	60
Y	10	15	25	50
Z	40	20	10	70
Total	70	45	65	`180

The probabilities are obtained by dividing respective events by the total.

	A	B	C	Total
X	0.111	0.056	0.167	0.333
Y	0.056	0.083	0.139	0.278
Z	0.222	0.111	0.056	0.389
Total	0.389	0.25	0.361	1

Question (2)

P(A) = 0.389

P(X) = 0.333

P(A|B) = P(A$\bigcap$B) / P(B)

= 0/ 0.25 = 0

P(A|X) = P(A$\bigcap$X) / P(X)

= 0.111 / 0.333

= 0.333

Question (3a)

None of the events are independent

Question (3b)

(X,Y) ,(Y,Z), (X,Z), (A,B) , (B,C), (C,A) are the pairs of mutually exclusive events

Question (3c)

Two events are said to be independent if P(A$\bigcap$B) = P(A) * P(B)

The values of P(A$\bigcap$B) are given below

	A	B	C
X	0.111	0.056	0.167
Y	0.056	0.083	0.139
Z	0.222	0.111	0.056

The values of P(A) *P(B) are given below

	A	B	C
X	0.13	0.083	0.12
Y	0.108	0.069	0.1
Z	0.151	0.097	0.14

As shown above none of the respective values in the two tavles are equal, so no two events are indpendent

For two events to be mutually exclusvie events P(A$\bigcap$B) = 0

Here (X,Y) ,(Y,Z), (X,Z), (A,B) , (B,C), (C,A) are the pairs of mutually exclusive events since the don't have any common elements in them or P(A$\bigcap$B) for all sets is 0