You Could Suffocate!

Probability Level 3

Imagine that you're a $5$ year old; lying on your newly-bought cosy SpongeBob bed-set.

Suddenly, as you are about to board the boat meant to float gently across your mind... you are struck by a frightful thought.

'What if all the air molecules in this room go to the other side of the room?'. you wonder.

'I'd suffocate.' Feeling this quite unlikely, you, already as sleepy as a koala, go to sleep.

Given that there are about $1.729 \times {10}^{26}$ air molecules in your bedroom; What would happen to your chances of suffocation, if the number were reduced to $1.618 \times {10}^{26}$ ?

Details & Assumptions:

$\bullet$ The composition of the air remains intact, that is, the percentage of oxygen molecules is always the same; no matter the number of air molecules.

$\bullet$ The room is isolated and has no connection whatsoever to the outer world.

Decrease Increase Remain the Same May Increase or Decrease

1 solution

Nayan Pathak
Jan 29, 2015

Let the probability of each molecule of going to the other side of the room be p,(taking the case equally likely) as p<1,so p^k<p^m,if k>m,which is the case here

You Could Suffocate!

1 solution

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