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Deserted Island – Survival Chances

You are stranded on a deserted island. There is little food on the island. By your guesses, you will last 10 days unless you can get rescued by a boat.

If the probability of seeing a boat in 30 days is 95%, what are the chances of seeing a boat in the next 10 days? Stated differently, how likely are you to survive the next 10 days.

Hint 1
Start with calculating the probability of “not seeing a boat in 30 days”.

Hint 2
1. Start with calculating the probability of “not seeing a boat in 30 days”. This is 10%

2. The probability  of “not seeing a boat in 30 days”is equal to the probability of “not seeing the boat in the next 10 days” and “not seeing the boat in the next 10 days” and “not seeing the boat in the next 10 days”.

Answer

 

1. Start with calculating the probability of “not seeing a boat in 30 days”.

This is 5%

2. The probability  of “not seeing a boat in 30 days”is equal to the probability of “not seeing the boat in the next 10 days” and “not seeing the boat in the next 10 days” and “not seeing the boat in the next 10 days

if p = probability of seeing the boat in the next 10 days, then

5%= ( 1 – p ) x (1 – p) x (1 – p) -> p = 63%

The probability of your survival is 63%

6


Stating the obvious here, but I enjoy riddles & puzzles. Anyone else also struggling with seemingly simple 5th grade math problems?

Comments to Deserted Island – Survival Chances

  • http://www.mindpuzzle.me Mark at MindPuzzle.me

    A tough probability question! A lot of people are fooled into thinking the probability of surviving (“ie seeing the boat”) on the island is merely a case of taking the 95% and dividing it by three. As you have three 10 day periods. I will let the professional try and explain why this cannot be done.

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