Math problem from squid game

[juandiaz]

Find probability there will be 3 players win glass bridge game (from 16 players)

 

[BigBeachBanana]

Would you please share your work/thoughts?
Have you learn about binomial distribution?

 

[juandiaz]

I think n(s)=2^16 because each one pass or die.
N(E)= 18C3

 

[BigBeachBanana]

I think n(s)=2^16 because each one pass or die.
N(E)= 18C3

Please define your variable, we don’t want to guess what your variables mean. What is n(s) and n(E)?

 

[BigBeachBanana]

First, I would find the probability of 1 person surviving, which is synonymous with successfully choosing the right glass 16 times.

 

[JayJay]

Can a player see, and therefore avoid, a panel broken by a previous player?

 

[juandiaz]

Please define your variable, we don’t want to guess what your variables mean. What is n(s) and n(E)?

Probability Formulas​

Probability = (Number of a Favourable outcome) / (Total number of outcomes)

P = n (E) / n (S)

Where P is the probability, E is the event and S is the sample space. Now, let’s looks at some very common examples.

 

[BigBeachBanana]

Probability Formulas​

Probability = (Number of a Favourable outcome) / (Total number of outcomes)

P = n (E) / n (S)

Where P is the probability, E is the event and S is the sample space. Now, let’s looks at some very common examples.

Can you answer the question @JayJay asked you? This will impact how you calculate your probability.

Can a player see, and therefore avoid, a panel broken by a previous player?

 

[juandiaz]

Yes next player see the result from previous player.

 

[BigBeachBanana]

Yes next player see the result from previous player.

It sounds like a hypergeometric problem, have you learned about it?

 

[juandiaz]

It sounds like a hypergeometric problem, have you learned about it?

Absolutely no.

 

[BigBeachBanana]

For n people to cross, 16 - n need to fall. A player only falls when their step is broken, so if 16 - n players fall, 16 - n steps are broken in the end. The probability a step is safe or broken is always 1/2, so since there are 18 steps total the probability 16-n steps break and exactly n players cross is [math]\frac{ \binom{18}{16-n}}{2^{18}}[/math].

 

[juandiaz]

For n people to cross, 16 - n need to fall. A player only falls when their step is broken, so if 16 - n players fall, 16 - n steps are broken in the end. The probability a step is safe or broken is always 1/2, so since there are 18 steps total the probability 16-n steps break and exactly n players cross is [math]\frac{ \binom{18}{16-n}}{2^{18}}[/math].

Thank you so much.
I’ll try to learn hypergeometric.

 

[sky2rain]

Individual survival prob doesn’t mean much in this problem because the more right choices people in front of you make, the higher your probability is to survive the game. Hence it is a changing probability for everyone except the first individual or whoever becomes the first individual after those before him all died.

If the question asks about the probability of exactly 3 player survives, it’s better to analyze the situation from the angle of how many people must be killed, which is 13 people, in this problem. With each player killed, you will have 1 step with a shattered glass. If we denote each step with both glass intact as 1, and with 1 glass shattered as 0, then you would form a binary string of 18 digits with 13 of them 0s denoting the death of 13 people. So 18c13 is the total combos that get exactly 3 people cross, which give you 8568 cases.

you cannot have 18c17 and 18c18 shattered steps because there aren’t that many people to kill. So the probability is simply 8568 / ( 2^18-18c17-18c18) = 8568/262,125 = 3.27%

 

[sky2rain]

However this doesn’t mean that the chance of survival is slim for 3 people out of 16 to survive. It’s the probability for exactly 3 players to cross. If you change the problem to calculate the probability for at least 3 players to survive, you will get a much larger probability.

 

[BigBeachBanana]

Here's the distribution for those who are interested: