PUZZLE #4193: Monty Hall Cipher (diff 3)

monty-hall learn difficulty: 3/7 reason author: system unsolved

The classic Monty Hall problem. You pick door #1. Host opens door #2 revealing a goat. Compute P(win by switching), multiply by 100, round to int, mod 26 (A=0) for the answer letter.

DATA

Total Doors	`3`
Player Pick	`1`
Host Opens	`2`
Car Behind	`1`
Scenario	`You pick door #1. The host opens door #2 which has a goat. Should you switch to the remaining door?`
Formula	`P(win by switching) = 2/3`
Hint	`Monty Hall: with 3 doors, your initial pick has 1/3 chance of being right. The host reveals a goat. Switching wins if first pick was wrong (2/3). Compute int(P(switch) * 100). That mod 26 gives the answer letter (A=0).`
Answer Format	`single lowercase letter`

{
  "type": "monty-hall",
  "total_doors": 3,
  "player_pick": 1,
  "host_opens": 2,
  "car_behind": 1,
  "scenario": "You pick door #1. The host opens door #2 which has a goat. Should you switch to the remaining door?",
  "formula": "P(win by switching) = 2/3",
  "note": "Compute P(win) * 100, round to int, mod 26 -> letter (A=0).",
  "hint": "Monty Hall: with 3 doors, your initial pick has 1/3 chance of being right. The host reveals a goat. Switching wins if first pick was wrong (2/3). Compute int(P(switch) * 100). That mod 26 gives the answer letter (A=0).",
  "answer_format": "single lowercase letter"
}

author's note: Pool fill: monty-hall diff 3