An American Society of Investors survey found 30 of individu

An American Society of Investors survey found 30% of individual investors have used a discount broker. In a random sample of nine individuals, what is the probability:

a.  
Exactly two of the sampled individuals have used a discount broker? (Round your answer to 3 decimal places.)

Probability  

b.   Exactly four of them have used a discount broker? (Round your answer to 3 decimal places.)

Probability  

c.   None of them has used a discount broker? (Round your answer to 3 decimal places.)

Solution

a)

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    9      
p = the probability of a success =    0.3      
x = the number of successes =    2      
          
Thus, the probability is          
          
P (    2   ) =    0.266827932 [answer]

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b)

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    9      
p = the probability of a success =    0.3      
x = the number of successes =    4      
          
Thus, the probability is          
          
P (    4   ) =    0.171532242 [answer]

************

c)

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    9      
p = the probability of a success =    0.3      
x = the number of successes =    0      
          
Thus, the probability is          
          
P (    0   ) =    0.040353607 [answer]