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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?

  Submitted by Ravi Raja    
Rating: 3.6250 (8 votes)
Solution: (Hide)
Using the binomial distribution, the probability that n flies out of 5 have been eaten is combin(5,n)*(1/2)^5, where combin(5,2)=5!/(n!*(5-n)!).

The probability that 0 flies were eaten is combin(5,0)*(1/2)^5=1/32.

The probability that 1 fly was eaten is combin(5,1)*(1/2)^5=5/32.

The probability that 2 flies were eaten is combin(5,2)*(1/2)^5=10/32.

So the probability that the spider is still hungry is 1/32 + 5/32 + 10/32 = 16/32 = 1/2.

The probability the spider is full is 1-1/2=1/2. Thus the probability of a successful attempt to pass is (1/2)*1 + (1/2)*0.5 = 0.75 .

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionPuzzle SolutionK Sengupta2009-02-26 15:34:03
AnswerK Sengupta2009-02-15 15:36:15
re(3): simpler computationSilverKnight2003-12-04 16:55:15
re(2): simpler computationBob Genisot2003-12-04 16:31:08
re: Easier than it sounds...Lee2003-12-03 23:57:12
SolutionEasier than it sounds...Magick3212003-12-03 22:53:38
Solution?Prab2003-11-28 00:30:00
spider and flyEd Lunn2003-11-26 18:19:49
noneLee2003-11-26 13:53:19
SolutionSolutionClinton Heath2003-11-26 12:24:57
re: Solution to a strange questionkrdmt5_0002003-11-25 16:23:48
SolutionSolution to a strange questionkrdmt5_0002003-11-25 16:18:30
re(3): simpler computationRobin Gatter2003-11-25 12:13:45
re(2): simpler computationCharlie2003-11-25 10:36:38
re: simpler computationSilverKnight2003-11-25 10:10:59
Solutionsimpler computationCharlie2003-11-25 09:58:41
re: just a little correction in my textSilverKnight2003-11-25 09:46:00
Solutionwell, I was wrong - corrected solutionSaso2003-11-25 09:45:18
just a little correction in my textSaso2003-11-25 09:23:40
SolutionsolutionSilverKnight2003-11-25 09:19:08
SolutionsolutionSaso2003-11-25 09:18:32
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