3.2. Axiomatic Definition of Probability

Try these first

1. 1.

   Define Sample Space.

   Hint

   Think about outcomes of tossing a coin.

2. 2.

   What is Normalization in probability?

   Hint

   Consider what happens when all possible events are accounted for.

3. 3.

   What is the probability of an event being negative according to Kolmogorov’s Axiom?

   • True
   • False

   Hint

   Think about the definition of probability.

4. 4.

   If the sample space S consists of four outcomes, what is the assigned probability if the outcomes are equally likely?

   • 0.25
   • 0.5
   • 1

   Hint

   Recall how probabilities are assigned in equally likely events.

5. 5.

   Consider a biased coin with P(H) = 0.7 and P(T) = 0.3. Using Kolmogorov's axioms, validate the probabilities.

   Hint

   Analyze the logic of probability assignments.

6. 6.

   Create a probability space for rolling two dice and determine probabilities for their sum resulting in 7.

   Hint

   Break down the sums for two dice to find the total possible outcomes.