Monty Hall

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TECHNICAL INTERVIEW QUESTION on PUZZLESThe
Monty Hall Puzzle
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2
The Monty Hall Puzzle
C
B
A

• You are the contestant on a Game Show. There are
  3 doors say A,B and C and behind one door is
  the prize of a million dollars. The prize is
  randomly placed and the probability of finding
  the prize behind any door is 1/3.
• You get to pick one door and if youve picked the
  right door, you win the prize.
• Theres a catch. After youve chosen a door, the
  game show host will not immediately open that
  particular door. The host will open another door
  that you did not pick and which he knows does not
  contain the prize. Suppose you had picked door A,
  and the prize is behind door B, the host will
  open door C and let you know that there is
  nothing being door C.
• At this point, you will be given a choice Do you
  want to stick with your original choice (door A
  in the example above) or do you want to choose
  the other unopened door (door B in this example)?
• Would you switch your choice?
• Do you think that switching doors would have any
  impact on the probability of finding the prize?

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The Monty Hall Puzzle

• Do you think that switching doors would have no
  impact on your odds of winning the prize?
• Do you think that the probability of finding the
  prize behind either door would be the same 50?
• WRONG!!
• This is a bit counter-intuitive but you should
  switch doors.
• Probability of winning the prize
• Sticking to your original choice 1/3
• Switching to the other door 2/3
• HOW?

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Simulating the Monty Hall Puzzle

• Let us assume without loss of generality that the
  prize is behind door A.

Stick to your Original Choice
Switch your Choice
You pick the other unopened door. You lose!
You pick Door A
The Host opens door B or C
You pick Door A. You win!
You switch your choice to door A. You win!
You pick Door B. You lose!
You pick Door B
The Host opens door C
You switch your choice to door A. You win!
You pick Door C. You lose!
You pick Door C
The Host opens door B
Net Odds of winning 2/3
Net Odds of winning 1/3
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Explaining the Monty Hall Puzzle
Lets the divide the doors into two sets Set 1
The door you picked originally The Probability
that the prize is in Set 1 is 1/3 Set 2 The
other two doors The Probability that the prize
is in Set 2 is 2/3 The Host will open a door
from Set 2 that does NOT have the prize, but the
probability that the prize is in Set 2 still
remains at 2/3. Switching your choice to choose
the remaining unopened door from Set 2 maximizes
your odds of winning.
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CodeGround Online Testing Platform is an online
assessment and evaluation system that helps
Recruiters conduct online screening tests to
filter candidates before the interview process.
CodeGround Recruitment Tests can be used during
Campus Recruitment or screening walk-in
candidates. CodeGround supports Aptitude Tests,
English Communication Skills Assessments and
Online Coding Contests in C, C, Java, PHP,
Ruby, Python and JavaScript. CodeGround also
supports asynchronous automated interviews.