The probability of having a babygirl is 5035 What is the pro

The probability of having a babygirl is .5035. What is the probability of having 2 or more daughters out of 3 children? What is the probability of 1 or fewer daughters out of 4 children?

Solution

a)

Note that P(at least x) = 1 - P(at most x - 1).          
          
Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    3      
p = the probability of a success =    0.5035      
x = our critical value of successes =    2      
          
Then the cumulative probability of P(at most x - 1) from a table/technology is          
          
P(at most   1   ) =    0.494750086
          
Thus, the probability of at least   2   successes is  
          
P(at least   2   ) =    0.505249914 [answer, 2 or more daughters]

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b)

Using a cumulative binomial distribution table or technology, matching          
          
n = number of trials =    3      
p = the probability of a success =    0.5035      
x = the maximum number of successes =    1      
          
Then the cumulative probability is          
          
P(at most   1   ) =    0.494750086 [ANSWER]