Amazon Interview Question - Coin on a Chess Board - Probability Puzzle

Amazon interview puzzle:
A coin of diameter 1 is thrown on to an infinitely large chessboard with squares of side 2. What is the chance of the coin enclosing two colours? So, you have to calculate the probability of the coin enclosing both black and white colors when it's landed on the board.
The intention of mentioning an Infinitely large chessboard is that we should not consider the edges of the board, rather we should just focus on the main board.
The difficulty level set by the composer of this puzzle is just 2 out of 5.
So, you must give it a try. Pause the video and think logically.

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[prakasha]

Questions are difficult, but solutions are simple, amazing....

[emponator]

Pretty bold to assume that there is no chance of the coin to land on it's edge. =D

[porth]

Amazon interview puzzle: you have a 10 minute break, the break room is 5 minutes walk from your work station, how long is your break in the break room?

[erikmartin]

I got the solution a different way which was easier to calculate: To cover 2 colors the coin must be crossing a vertical vertex, a horizontal vertex, or both. Whether it's crossing a vertical or horizontal vertex are independent probabilities, if the coin is placed randomly. The coin can travel a distance of 1 while across a vertex, and a distance of 1 between vertexes, so the probability of it being on a vertex in 1 dimension is 50%. So the probability of being on neither vertex would be 50%*50%, which is 25%, so the probability of it being on at least one vertex and thus covering 2 colors is 1-25%, so 75%.

[ankanathharsha]

PLEASE KEEP UPLOADING RIDDLES CONSTANTLY>>
YOU CAN MAKE THIS CHANNEL THE RIDDLE ENCYCLOPEDIA

[jounik]

Check the effect of x and y positions of the coin independently. In both directions there's a repeated cycle of length 1+1, where the coin is over a (horizontal/vertical) line or between lines.
So the probability of being between lines in both directions is 1/2 * 1/2 = 1/4. The opposite is the coin being on a horizontal or vertical line, probability:
1 - 1/4 = 3/4.

[arjunannamalai.m]

I got the answer without seeing the answer 🤩

[dvorszkydavid]

Hey!
I used Inclusion–exclusion principle and got the same result. (P(A): probability of enclosing vertically, P(B): probability of enclosing horizontally. P(A)+P(B)-P(AB) = 0.5+0.5-0.25 = 0.75)
Is this a valid solution or was it just blind luck?

[michalljubljanac]

The problem seems to be ill-posed. Nothing indicates that the coin's center should land on the central square. If we assume that it can land anywhere on the board, we get a completely different probability since squares around the seams have a smaller area adjacent to other squares. If I got this kind of interview question and the interviewer insisted that this is the correct solution I would be rightfully pissed.

[pranaykumar]

Bro I have a doubt with your answer...
75% probability is satisfying with all the squares but not with the 4 edges right 🙄

[baskarp]

Super and clear cut explanation🔥 Teaching speaks 👌 Continue this to give us knowledge

[manusarda]

I will rate It 3/5
Because it took almost 3-4 min to solve.
Who else was able to solve????

[saurav_kr]

Here we have an another amazing video 👌👌👌 Keep it up. But please reduce your uploading period.

[AyrtonTwigg]

And to make the probability 50%, the squares would need a side length of around 2.414

[bluemalamute]

How about this one? Imagine the universe is filled with alternating cubes of chocolate and vanilla ice cream with edge length 2. Suppose we can randomly extract a unit spherical scoop. What is the chance of getting only chocolate?

I'm figuring within a given flavor cube, there's a unit cube where the center point of the scoop can be and get only that flavor. So, to get only chocolate, you have .5 [prevalence of chocolate] * (1/8) [volume of target cube/volume of flavor cube] = 1/16 chance of only chocolate.

[himanshusaini]

As I opened the VDO eventually it's speaks out from my mouth
What's up logical people this is Ammar

[jitenvadhavana]

Use this formula
d(2x -d) / x^2

Where,
d: coin diameter
x: side of square

[tamirerez]

One more excellent video from the factory or AMMAR'S LOGIC INDUSTRIES.
thank you ammar for a very nice riddle, not very hard, but very nice.
btw, what is the chance of this coin to cover only 1 white area, and 1 black area?
(I mean not, for example, on the cross middle of 4 squers, forming 2 white and 2 black areas, like the logo of BMW, and not near the corner, covering 2 black areas and 1 white)
What is the chance to cover ONLY 1 white and 1 black areas? That problem is turning the riddle from Amazon interview question, into NASA interview question...
Can you please, make part 2 to this video, which in you show the answer to my challenge?
Thank you Ammar for very good video, and very simple explanation!

[ABCXYZ-ztdr]

Awesome puzzle
My ans is also 75% but different approach
My approach= largest circle that can come inside that square " r=1"
"Area= π"
Area of that coin =0.25π
Probability that coin come inside the square= Area of coin/area of big circle
=0.25
Probability that coin does not come inside square= 1-0.25=0.75
"75%"
Please leat me know weather my approach is correct or not

[Galois]

Hi Ammar, can you put some riddles from Smullian plz?