Posted by **Mujtaba** on Saturday, January 5, 2013 at 3:39am.

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.

- Probability -
**MathMate**, Saturday, January 5, 2013 at 12:06pm
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.

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