Question

For given list of members in a universal set U.

Members A B

1 a1 b1

2 a2 b1

3 a3 b2

4 a1 b2

5 a1 b2

6 a2 b1

7 a3 b1

8 a1 b2

9 a1 b2

10 a3 b2

Write Probability distribution table for

(a) P(A, B)

(b) P(A)

(c) P(B)

(d) P(A|B=b1)

Answer 1

For given list of members in a universal set U.

Member	A	B
1	a1	b1
2	a2	b1
3	a3	b2
4	a1	b2
5	a1	b2
6	a2	b1
7	a3	b1
8	a1	b2
9	a1	b2
10	a3	b2

Write Probability distribution table for

(a) P(A, B)

Number of cases of ( A, B ) = { a1 b1 , a2 b1, a3 b2, a1 b2, a3 b1 } = 5

To calculate probability of each case divide the number of occurances by 10.

Member	a1 b1	a2 b1	a3 b2	a1 b2	a3 b1
Probability	1/10	2/10	2/10	4/10	1/10

(b) P(A)

Number of cases of ( A ) = { a1 ,a2, a3 } = 3

To calculate probability of each case divide the number of occurances by 10.

Member	a1	a2	a3
Probability	5/10	2/10	3/10

(c) P(B)

Number of cases of ( B ) = { b1 ,b2 } = 2

To calculate probability of each case divide the number of occurances by 10.

Member	b1	b2
Probability	4/10	6/10

(d) P(A | B = b1)

Number of cases of (A | B = b1) = { a1 b1, a2 b1, a3 b1 } = 3

To calculate probability of each case divide the number of occurances by 4 since total number of cases of b1 is 4.

Member	a1 | b1	a2 | b1	a3 | b1
Probability	1/4	2/4	1/4