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Spider and Fly (Posted on 2003-11-25) Difficulty: 3 of 5
A spider eats 3 flies a day. Until the spider fills his quota a fly has a 50% chance of survival if he attempts to pass the web.

Assuming 5 flies have already made the attempt to pass, what is the probability that the 6th fly will survive the attempt?

See The Solution Submitted by Ravi Raja    
Rating: 3.6250 (8 votes)

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Solution solution | Comment 2 of 21 |
Given that the spider has not yet reached his quota, the fly will have a 50% chance of getting through... but we don't know whether or not the spider has reached his quota from the first 5 flies...

So, there are several possibilities that the spider could have reached his quota within the first 5 flies:
(let C = caught, and N = not caught)

Here they are, along with the likelihood of them occuring:

CCC = 1/8 = 4/32
CCNC = 1/16 = 2/32
CCNNC = 1/32
CNCC = 1/16 = 2/32
CNCNC = 1/32
CNNCC = 1/32
NCCC = 1/16 = 2/32
NCNCC = 1/32
NCCNC = 1/32
NNCCC = 1/32

These are ALL the possibilities (I think) of the spider having caught his fill for the day.

Now, if we total this up, we show there is a 1/2 chance that the spider has already caught his fill.

If he has, then he won't attempt capturing the fly.... and if he hasn't, there is a 50% chance he'll capture the fly...

The question asked... what's the probability the fly will make it... so
1/2 * 50% + 1/2 * 100% = 3/4
  Posted by SilverKnight on 2003-11-25 09:19:08
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