Assume that P ( A ) = P ( B ). Show that A = B

Solution:

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

For an experiment having n number of outcomes, the number of favorable outcomes can be denoted by x.

Let P (A) = P (B)

Let x ∈ A

A ∈ P (A) = P (B)

Therefore,

x ∈ C, for some C ∈ P (B)

Now, C ⊂ B

Hence, x ∈ B

So, A ⊂ B

Similarly, B ⊂ A

Therefore, A = B proved

NCERT Solutions Class 11 Maths Chapter 1 Exercise ME Question 6

Assume that P ( A ) = P ( B ). Show that A = B

P (A) = P (B) is given. We have proved that A = B