DSE 2009

[Ashima]

Hi Sir,

Can you please explain how I should solve this problem?

Consider tow events A and B with P(A) = 0.4 and P(B) = 0.7. The maximum and minimum values of P(A intersection B) respectively are:

a. 0.4, 0.1
b. 0.7, 0.4
c. 0.7, 0.1
d. 0.4, 0

[PRIYANKA]

hi ashima
P(AUB) = P(A) + P(B) -P(A INTERSECTION B)
= 0.4 +0.7 -P(A INTERSECTION B)
=1.1- P(A INTERSECTION B)

SO MIN VALUE IS .1

AND p(A) = 0.4  , p(B) = 0.7
SO MAX VALUE IS .4

[Ashima]

Hi Priyanka,

Thanks for the reply:)

I did not understand how did you get max value equal to 0.4?

[Amit Goyal]

Its simple. A INTERSECTION B is a subset of both A and B and hence P(A INTERSECTION B) can take value less than or equal to min{P(A), P(B)} = 0.4. The max value it can take is thus 0.4.

[Ashima]

Thank you sir:)