[Community Puzzle] Kiss the girls

How did you get 7? Can you explain me please?

I was getting 7 because I was doing the calculation incorrectly. I was naively just adding up the cumulative risk, which caused it exceed the limit more quickly.

what should you do then

Somebody above pointed out to me that if you flip a coin twice in a row, the possibility of hitting the same thing twice is not 100% (i.e. 50% + 50%). It is actually only 25% as there are only four possible outcomes.

There is a formula for calculating combined probabilities.

let’s supposed the events :

  • A : catching monkeypox from the girl A
  • B : catching monkeypox from the girl B

the Probability of catching monkeypox from two girls (A,B) is :

P(A U B) = P(A) + P(B) - P(A ∩ B)   (1)

Where :

  • P(A) = min(x_A,y_A)/(x_A² + y_A² + 1)
  • P(B) = min(x_B,y_B)/(x_B² + y_B² + 1)
    and since the event A is distincts from the event B then we can say that :
    P(A ∩ B) = P(A) * P(B) (2)
  1. to calculate the Probability of Three girls (let’s say A,B ,C) : ( using (1) and (2) )
 P(AUBUC) = P((AUB) U C)
          = P(AUB) + P(C) - P(AUB) * P(C)

and so one(recursively) until you find the solution

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The great thing about this puzzle is, if you didn’t know how to solve it going in, you’ve learned something that will fundamentally change the way you look at the world.

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