In an assembly of 200 people there approximately 2% of them are civil engineers. If we randomly select five people, what is the probability of them being civil engineers?

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stomachdm · Accepted Answer

Step 1  Binomial random variable follows the conditions given below.  1. The number of trials n are fixed.  2. The possible outcomes for each trial is 2.  3. Each trial is independent.  4. The probability of success in each trial is equal.  The probability mass function for binomial distribution with n trials and p probability of success is given by the formula P(x)=(nx)⋅px⋅(1−p)n−x. The mean of binomial distribution is given by μ=n⋅p.  Step 2  2% people are civil engineers so there is 0.02 probability that a randomly selected person is a civil engineer. The total number of people selected is n=5 which is number of trials and each person is independent to other so trials are independent.  There are two possible outcomes either the person will be civil engineer or not and the probability of success for each trial is p=0.02. If x is the number of people who are civil engineers out of 5 selected person then the x will follow binomial distribution.   It is asked to find the probability of x=5 and to compute this probability substitute all the values in P(x)=(nx)⋅px⋅(1−p)n−x  P(5)=(55)⋅(0.02)5⋅(1−0.02)5−5  =5!5!⋅(5−5)!⋅(0.0000000032)⋅1  =3.2×10−9  So probability that all of them are civil engineer is 3.2×10−9.

Marcus Herman · Accepted Answer

Step 1   Given  n=200  p=2%=0.02  x= no. of people being civil engineers  P(X=x)=CxnPx(1−p)n−x;x=0,1,…,n  Step 2  The probability of 5 people being civil engineers is  =P(x=5)  =C5200(0.02)5(1−0.02)200−5  =0.15788

In an assembly of 200 people there approximately 2% of

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