suppose two players play a traditional russian roulettes game one bullet is put into a 6 revolve

Step 1: In a traditional Russian Roulette game with one bullet in a 6-revolver, it is always bet

Suppose two players play a traditional russian roulettes...

Suppose two players play a traditional Russian Roulette game. One bullet is put into a 6-revolver, and the barrel is randomly spun so that there is an equal chance for each chamber to be under the hammer. Two players take turns pulling the trigger against themselves until one kills themselves. Under such rules, would you rather go first or second? What's the probability of survival if you go first? b) Now the rule is changed, and the barrel gets spun after each shot. Now, would you rather go first or second? What's the probability of survival for each choice? c) Suppose two bullets, instead of one, are randomly put into the chamber. Your opponent went first and survived the shot. Now you are given the chance to spin the barrel. Should you do it or not? d) What if the two bullets are consecutively put into the chamber, and the barrel is spun (i.e., two bullets are next to each other)? Should you spin again after your opponent survived the first round?

Transcript

00:01 What a gruesome problem, but anyway, suppose two players play a traditional russian roulette game.

00:08 One bullet is put into a six revolver, and the barrel is randomly spun, so there's an equal chance for each chamber to be under the hammer.

00:16 Two players take turns to pull the trigger against themselves until one kills him or herself.

00:21 Under search rules, would you rather go first or second? i would always go second.

00:26 Let that first person be the possibility, because if they lose, you win.

00:31 So you always go second.

00:34 What is the probability of survival to go first? well, b5 empty chambers out of six in total chambers.

00:43 Total chambers.

00:44 So that's a.

00:45 Now for part b, suppose the rule is changed.

00:48 A barrel gets spun after each shot.

00:50 Now would you rather go first or second? you always go second.

00:55 What is the probability of survival for each? choice.

01:02 So, okay, so if you go first, your probability is going to be five out of six.

01:07 Okay, so if you end up going second, that means the first person survived, and we're going to spin it again, so that means this probability is still five out of six.

01:18 So part c, suppose you have two bullets instead of one, and you randomly put them in the chamber.

01:24 Your print opponent went first and survived.

01:26 Now you were giving a chance to spin the barrel.

01:29 Should you do it or not? well, if he survived, that means four out of six.

01:35 He survived.

01:36 But he used one of those chambers.

01:39 So that means that if you don't spin it, you're not going to include his chamber and there's only going to be five.

01:46 So your probability, if you don't spin, would be three out of five.

01:51 If you don't, if you do spin, it's going to be four out of six.

01:56 What is this going to be? this is 0 .6%.

01:59 This is 0 .67%.

02:02 Spin that chamber again.

02:04 So part d.

02:05 We have what if two bullets are consecutively put into the chamber and the barrel is spun.

02:11 In other words, the two bullets are next to each other.

02:13 So bullet, bullet, no bullet.

02:17 Okay.

02:18 Should you spin again after your opponent survive the first round? so your opponent.

02:26 Have survived the first round, which means he got one of these four.

02:30 So if he survived, you need to know what's the probability of there being a bullet after that.

02:36 So probability of a bullet, given that he's already survived.

02:41 So a blank, then a bullet.

02:44 So what is our probability there? so we already know that he had a blank.

02:48 So that would be four out of six would be that probability.

02:52 What's the probability there being a bullet in the next one? that would be a be two out of five.

02:58 So we would reduce that.

02:59 Let's get that three.

03:01 So that's going to be four out of 15.

03:04 Now if you spin it, that's if you don't spin it.

03:07 If you spin it, then the probability is simply going to be four out of six...

Question

Please give Ace some feedback