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im still wondering what any of these questions have to do with actual trading? If you could apply math to trading then computers would do all the work LOL

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umm i cant answer that question but i know i love trading and know how to trade... where does this leave me?

is it 0%? im clueless

@trading4ever ... i would bet a buffalo nickel that you are a competent trader. however, the harsh reality is that if you want to trade for a prop most of them filter their candidates via probability brain teasers. so, if u just want to "etrade", then this thread is irrelevant. however, if u want to go into prop trading then i recommend you sharpen your prob brainteaser abilities !

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A coin has to land in a square. Every square is 10 x 10cm. For a 1 cm circle to land on a line, the center of the circle has to be

jhoratio is right about the methodology, but he missed a couple of things in the specification of the problem:

• 1cm is the radius, not the diameter;
• It has to land in a white square.

Because it's a 1 cm radius, it's 8x8 not 9x9 (so 64% probability of landing entirely in a square rather than 81%), and because it has to land in a white square, you have to cut that in half (so 64% becomes 32%).

Nice Hoover. Ok next question? A tech company is about to announce important news and the stock can either go up to 100 or down to 50 after the news. It has a 80% chance of being good news. What is the stock worth right now? Assume the efficient market hypothesis holds here.

Once you figure out the answer to that, assume there's a call option and put option with the same strike as the correct answer above. What are they worth? Assume interest rates are 0, there is no volatility, no friction, etc. Also, what is the straddle with this same strike worth?

stock = (.8)(100)+(.2)(50) = 90 call = (100-90)(.8) = 8 put = (90-50)(.2) = 8 straddle = 8+8 = 16

Question 1(logic):

Ok we have $1 on the table and a quarter. Every time we flip the coin and it lands on heads, the money on the table doubles but once it lands on tails, the money on the table goes to 0 and the game ends. You keep all the money on the table and can stop the game whenever you want. How much would you pay to play this game?

Question 2 (algo):

There is a new prison with 100 prisoners and 100 prison cells. All the prison cells are the same except 1 special room which has a light switch you can turn on and off in the room. (assume only the prisoners can use the switch and the prison guards can not touch the switch) The rest of the cells have no lights and prisoners never see each other, can not see each others cells, and thus can not communicate to each other once they go in (aka they can only communicate via the special room and light switch). During the daytime, the prisoners come out of the cells and then at night, they are assigned a random room. (no limit on going into the same cell)

Before the prisoners go in, The Warden asks the prisoners to develop a strategy given the parameters above in which everyone has been to the special cell at least once at which point any prisoner can declare to the Warden that every prisoner has done so. If the prisoner is right, every prisoner is released out of jail and if the prisoner is wrong, everyone is executed. What strategy should the prisoner use so that everyone is released and at what night do you have a 100% confidence level that everyone has been in the special cell given your strategy?

Question 3 (game theory):

There are 3 people in the room: you the interviewee, interviewer A, and me. We all have guns and the object of the game is survival of the fittest and only 1 person can survive. You shoot first, then interviewer A, then me and it keeps going in that cycle until last person standing. When you shoot, you hit 50% of the time, when interviewer A shoots he hits 75% of the time and I never miss. Assuming game theory here (everyone behaves in their own best interest/optimally for themselves). Since you shoot first, what is your strategy to optimize your chance of surviving and what is the probability that you survive using your optimal strategy?

1 you are risking x to win x 50% of the time which has 0 EV so I'd pay anything less than $1 and take the risk free dollar

2 can the prisoners discuss the strategy beforehand?

3 If I shoot A you are up next and im dead 100%. If I shoot you A is up next and I've got a chance of him missing, so that's the best option if I have to shoot. Though ideally I'd not shoot or intentionally miss.

If I don't shoot A will go for you since killing me would lead to you killing him 100%. If A goes for you and hits, I get a free shot on A. If A misses you, you kill him because whoever you don't kill gets a free shot at you and he is more accurate. I then get a free shot on you. Either way my chance of survival is >50% which is way better than my chances if I have to take a real shot first.

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2 The prisoners could agree to a light flicker counting system where if you are in the special cell for the first time you add one flicker to the count. So first guy flicks the lights on/off once, next guy in there for the first time flicks twice, etc. If they have been there before they just repeat the previous count. Once someone flicks the lights 100 times everyone has been in the cell with 100% confidence (assuming they are all incapable of forgetting the count, and wouldn't mess things up to kill everyone, which I guess is optimistic).

Not sure where I was off on #1, maybe someone else knows.

is 1. $0.625?

@ jnxpn nobody can see the special cell, they have no way of communicating so flicking once or twice doesn't really do anything. anyways, how did you like the internship? i encourage you to apply some prop firms this fall or ignore me if you have an offer from one already =)

@oreos, incorrect

oops, well then I guess you could have 99 people turn the light on if its their first time in the special cell with the light off and one guy turn the light off every time and keep track of how many times he did it until he reaches 99. Not sure if there is a more efficient way though.

Sending a PM

@ ivysaur

1. Really? First of all, this is hypothetical which is quite obvious because I said assume the efficient market hypothesis holds here which does not hold in the real world. Second of all, securities such as stocks/bonds/etfs have fair values regardless of what the bid/offer is and where you can execute a buy or sell. Although for stocks it tends to be very hypothetical/subjective. Most prices are just last sales and do not reflect anything beyond that. The market or bid/offer can be away from the last sale. Market makers could be fading the market to 10 basis points under fair value, for example, because they are holding too much long and they want more edge before they accumulate more inventory and there is no way to get out at 0 (such as redemptions with ETFs with no creation/fixed costs) That does not mean fair value is 10 basis points below fair value; fair value is fair value but you don't trade so you obviously don't get this.

2. I didn't know expiration dates mattered when there is no basis as clearly stated in the fucking question. A more intelligent question would have asked me to address the greeks which I should have said to assume the greeks are immaterial. Also learn to read.

3. Really? I'm not even going to respond to that given how fucking stupid you are.

Maybe you should go back to school but at the very least, learn to read before you speak. Please tell me you trade; I could use an easy dollar. I'm done with this thread.