According to government data 20 of employed women have never

According to government data, 20% of employed women have never been married. If10 employed women are selected at random, what is the probability
a. That exactly 2 have never been married?
b. That at most 2 have never been married?
c. That at least 8 have been married?

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 =    10      
p = the probability of a success =    0.2      
x = the number of successes =    2      
          
Thus, the probability is          
          
P (    2   ) =    0.301989888 [ANSWER]

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b)

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    10      
p = the probability of a success =    0.2      
x = the maximum number of successes =    2      
          
Then the cumulative probability is          
          
P(at most   2   ) =    0.677799526 [answer]

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c)

Note that P(at least 8) = 1 - P(at most 7).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    10      
p = the probability of a success =    0.2      
x = our critical value of successes =    8      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   7   ) =    0.999922074
          
Thus, the probability of at least   8   successes is  
          
P(at least   8   ) =    0.0000779264 [answer]