The Solution to the Official Math Problem!

There are 100 Snakes on the Plane. There are 100 Passengers on the Plane. Each Snake will Bite One Passenger at Random. What is the Probability that The Target, Mr. X, does not get bit?

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1. Suppose the Snakes are Labeled as S1, S2, S3…S100
2. Let’s look for a moment at Snake S1:
   • P(Snake S1 Bites Mr. X) = 1/100
     • In other words, there’s a 1/100 chance that Mr. X will get bitten by that particular Snake, S1
   • P(Snake S1 does not Bite Mr. X) = 1 – 1/100
     • This is the complement of a) above }
3. Notice that the logic of [2] applies to each Snake. That is,
   • P(Snake S1 does not Bite Mr. X) = 1 – 1/100
   • P(Snake S2 does not Bite Mr. X) = 1 – 1/100
   • P(Snake S100 does not Bite Mr. X) = 1 – 1/100
4. Thus, P( Mr. X does not get Bitten ) = The Product of all the Probabilities in [3],
   • (1 – 1/100) x (1 – 1/100)   x … x   (1 – 1/100)
   • S1 no Bite & S2 no Bite & … & S100 no Bite
5. So, the Final Solution for P(Mr. X Not Bit) = (1 – 1/100)¹⁰⁰ ≈ 36.6%

*Note* that we are assuming independence in Step [4], we’ll leave it to the Biologists to interpret whether this is a reasonable assumption