Recent content by Gavran

My three favorites:

I would rather use “Suppose there are ## n ## possibilities and those (precisely) ## n-1 ## must happen.” Therefore, if the USA wins, two events happen: the first one is “Great Britain does not win” and the second one is “China does not win”. The event “the USA does not win” does not happen...

5/5 5/5 3/5 3/5 1/5 5/5,5/5 5/5 2/5 5/5

Your results are correct. The expected value of a profit (or a loss) in the case of a fair bet must be equal to zero. ## E(\text{Profit}_{Ra})=3\cdot P_{Ra}(sun)-2\cdot P_{Ra}(rain) ## ## E(\text{Profit}_{Ra})=3\cdot 2/5-2\cdot 3/5 ## ## E(\text{Profit}_{Ra})=0 ## ##...

The third method from the original post is criticized mostly for the case in which player A has one winning round and player B has a zero winning round when the interrupting event occurs. Applying the third method in this case, the whole prize pot is awarded to player A, although he has only one...

There are many versions of this problem with different scores and different interrupting events. One interesting scenario is a scenario when the game is interrupted by police because the game is organized illegally. The original problem statement is “A company [two players] plays a ball game to...

@symbolipoint, thank you. In any of the earlier posts, nobody mentioned the solution for ## 0^0 ##. Using post #8 for defining ## 0^0 ## will generate the result ## 0^0 =0^{x-x}=0^x/0^x=0/0 ##, which is undefined. The mathematical expression ## 0^0 ## has different interpretations, and it is...

Two players, A and B, are playing a game, and the probability that either player wins a round is 1/2. They contribute equally to a prize pot. The game ends when one of the players wins six rounds. The game is interrupted for some reason when player A wins 5 rounds and player B wins 3 rounds. How...

Can you provide any reference where these methods are called "multiplication and division by numerical trituration"?

The formula ## f=(\pi/5+\sin72^\circ/2-2\sin72^\circ\sin^236^\circ)/(\pi/5+\sin72^\circ/2)\\ ## from post #6 can be transformed into a general case. ## \begin{align} f=&(\pi/n+\sin(2\pi/n)/2-2\sin(2\pi/n)\sin^2(\pi/n))/(\pi/n+\sin(2\pi/n)/2)\nonumber\\...

You are correct. Mechanical energy can be potential energy too. Elastic energy is the mechanical potential energy, but it does not affect the categorization that I mentioned in post #3. The same holds for electrical energy. There is energy of charges due to their position in an electric field...

I am unsure of what to say here. There are those who will tell you that Vbf is equivalent to Vb - Vf, and there are those who will tell you that Vbf is equivalent to Vf - Vb. If your choice is Vbf=Vf-Vb, your calculations are correct. The points B and C are at the same potential, so you can...

You ask about the difference between thermal energy and mechanical energy. Both are two different forms of kinetic energy, which is the energy of motion. All types of kinetic energy can be categorized as radiant energy, thermal energy, sound energy, electrical energy, and mechanical energy...