Let S={s1,s2,s3,s4}

Question

Let S={s1,s2,s3,s4}
be a sample space with probability distribution P,
given by 
P(s1)= 0.5, P(s2)= 0.25, P(s3)= 0.125, P(s4)= 0.125.

There are sixteen possible events that can be formed from the elements of 'S'.
Compute the probability and surprise of these events.

MathMate · Answer

I assume that each of the sixteen events has two outcomes of S, namely
P(s1,s1), P(s1,s2).....P(s4,s4).
By the multiplication rule, and assuming that the two outcomes are independent, we have
P(s1,s1)=P(s1)P(s1)=0.5*0.5;=0.25
....
P(s4,s4)=P(s4)P(s4)=0.125*0.125=0.015625
Note: The sum of probabilities of the 16 events should add up to 1.
Not sure about the surprise part.

Let�� �S={s1,s2,s3,s4}

Let�� S={s1,s2,s3,s4}