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Probability of Getting a Job

Date: 7/10/96 at 18:52:11
From: Anonymous
Subject: Probability with Different Events

If a person is applying for five different jobs and has a ten percent 
chance of getting any one job, what is the probability of getting any 
job at all? 

I eliminated adding the probabilities, so I know my odds aren't 
50 percent.  Then I thought maybe the odds are only as good as your 
probability of getting the highest likelihood for a job, in this case 
10 percent.  But it seems as if there must be some benefit in applying 
for more jobs.  Do you multiply the odds, i.e. 
.9*.9*.9*.9*.9 = 45 percent chance of not getting any job?. 

Date: 7/10/96 at 20:6:33
From: Doctor Anthony
Subject: Re: Probability with Different Events

Note that in the situation you describe you could end up with 
0, 1, 2,...5 jobs, so giving 6 possible outcomes.  If you wanted the 
probability of say 3 jobs you would use the binomial probability 
   P(3) = 5C3*0.10^3*0.9^2 = .0081  
  {where 5C3 = 5*4*3/(1*2*3) = 10}

However, the easiest way to tackle this type of probability is to 
consider that the probability of at least one job is 1 - prob.(no job)

       = 1 - 0.9^5

       = 1 - 0.59

       = 0.4095

-Doctor Anthony,  The Math Forum
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Associated Topics:
High School Probability

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