Question

If P(A)=1/12,P(B)=1/3,P(AB)=1/12, then P(A+B)=?

Answer 1

ANSWER

Going by options:

(a) Minimum value of P(A∩B) is the higher of P(A) and P(B) i.e.

3

2

and maximum value is 1. So, (a) is true.

(b) Maximum intersection of P(A∩

B

ˉ

) is the minimum of P(A) and P(

B

ˉ

) i.e. minimum of

2

1

and

3

1

=

3

1

. So, (b) is true.

(c) P(A)+P(B)=

2

1

+

3

2

=

6

7

. Hence, P(A∩B)≥

6

7

−1=

6

1

.

Again, maximum intersection of P(A∩B) is the minimum of P(A) and P(B) i.e. minimum of

2

1

and

3

2

=

2

1

. So, (c) is true.

(d) Maximum intersection of P(B∩

A

ˉ

) is the minimum of P(B) and P(

A

ˉ

) i.e. minimum of

3

2

and

2

1

=

2

1

.

Again, P(

A

ˉ

)+P(B)=

2

1

+

3

2

=

6

7

. Hence, P(

A

ˉ

∩B)≥

6

7

−1=

6

1

. So, (d) is true.

Hence, (a), (b), (c), (d) are correct.