Question

If a and b are events and b ⊂ a, why is it "obvious" that p(b) ≤ p(a)?

Answer 1

Answer:

If a and b are two events such that:

b⊂a

Then it is obvious that p(b)≤p(a)

where p denotes the probability of an event.

" Because as one event is contained in the other that means it has possibility to contain more favourable outcomes than the other while the probability of both the events is calculated by taking the total number of outcomes to be equal "

Let us consider an example as:

We roll a die;

so the total outcomes are: {1,2,3,4,5,6}.

Now let b denotes the event that the number is an even number less than 5.

Number of favourable outcomes( {2,4} )=2

p(b)= 2/6

let a denotes that the number is less than 5.

Then Number of favourable outcomes( {1,2,3,4} )=4

p(a)=4/6

clearly b⊂a

also we could see that p(b)<p(a)