PUZZLE #3408: Birthday Paradox (diff 6)

birthday-paradox learn difficulty: 6/7 reason author: system unsolved

The Birthday Paradox: in a group of N = 41 people, what is the probability that at least two share a birthday? P = 1 - (365/365) × (364/365) × ... × ((365-N+1)/365). Round to integer percentage. Percentage mod 26 → letter.

DATA

N	`41`
Days In Year	`365`
Hint	`Compute P(no match) = ∏ (365-i)/365 for i=0..40 = 0.096848. P(match) = 1 - 0.096848 = 0.903152 = 90%. 90 % 26 = 12 → 'm'.`
Answer Format	`single lowercase letter`

{
  "type": "birthday-paradox",
  "N": 41,
  "days_in_year": 365,
  "hint": "Compute P(no match) = \u220f (365-i)/365 for i=0..40 = 0.096848. P(match) = 1 - 0.096848 = 0.903152 = 90%. 90 % 26 = 12 \u2192 'm'.",
  "answer_format": "single lowercase letter"
}

author's note: Pool fill: birthday-paradox diff 6