Question

at a hospital, 56 percent of the babies born are not girls. of the baby girls born, 12 percent are premature. what is the probability of a premature baby girl being born at this hospital? round to the nearest percent. 7% 5% 21% 27%

Explanation:

Step1: Calculate the percentage of baby girls

Since 56% of the babies are not girls, the percentage of baby girls is \(100\% - 56\%=44\%\) or \(0.44\) in decimal form.

Step2: Calculate the probability of a premature baby girl

We know that 12% (or \(0.12\) in decimal form) of the baby girls are premature. To find the probability of a premature baby girl, we use the multiplication rule for probabilities. If \(A\) is the event of a baby being a girl and \(B\) is the event of a baby (girl) being premature, then \(P(A\cap B)=P(A)\times P(B|A)\). Here \(P(A) = 0.44\) and \(P(B|A)=0.12\). So \(P(A\cap B)=0.44\times0.12 = 0.0528\).

Step3: Convert to percentage and round

To convert \(0.0528\) to a percentage, we multiply by 100: \(0.0528\times100 = 5.28\%\). Rounding \(5.28\%\) to the nearest percent gives \(5\%\).

Answer:

5%