Roulette Player
Russian Roulette (probability)?
Let's say two people are playing Russian roulette. Each player takes turns shooting the gun, which is spun after each shot and the game ends when someone dies. The gun has 6 rooms, and a ball is used. What is the probability that the winner the first person? Well, I p = probability that the first person dies. If he survives the first round, the probability of dying must be 1-p. So, p = 6.1 + (1-p) p = 7 / 12 Is this true? In response to the first answer, and yes every time you go you have a 1 / 6 chance to die, but you play until someone loses. The person who begins to have a greater chance of dying because he pulls the trigger time more.
No, it is not. Your first equation does not make sense at all in the calculation. * You must multiply the probability if the events are sequential. Second, we must remember that the game can continue forever if the two of them are lucky. But first I want to say, there are still 5 empty chambers in the barrel, right? In this case, here is my calculation: The probability the first person dies in the first round: p_1 = 1 / 6 It was the second turn: = p_2 (06/05) * (06/05) * (6.1) It arrives in the nth round: p_n = (1 / 6) * (5 / 6) ^ (2n) So, the probability that the first person dies, it's just a simple sum of all because they are all exclusively occurring event: p = p_1 + p_2 +...+ p_n P_3 + ... = (1 / 6) * (1 + (5 / 6) ^ 2 + ... + (6.5) ^ (2n) + ... ) = (1 / 6) / (1 - (5 / 6) ^ 2)) = 6 / 11. This result may be the same for someone else, but the underlying concept is different to start! The sum and multiplication of probabilities are fundamentally linked to events question and must be well understood. ===== Edit in response to Mr. FMS. I'm sorry I was a little harsh above. Here is my answer honest and friendly with Mr. FMS, sir equation p = 1.6 + (5.6) ^ 2p has a problem. If it was a correct equation, so how do you explain the equation for the second person dies, 1-p = (6.5) (6.1) + (6.5) ^ 3 (1-p) does * not * lead to the response, p = 6 / 11? Or, how do you know that p = 6.1 + (6.5) ^ 2 (6.1) + 4p ^ (6.5) is * not * the right equation? Since rational numbers math level Junior is quite simple, this kind of lucky mistakes happen all the time. You, sir, are not paranoid. I was * not * sufficient to explain nature in detail.
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