Question

in 2017, allegheny county reported 12,958 babies born.
a local pediatrician examined 288 babies and found that 24 had green eyes, 52 had hazel eyes, and 72 babies had blue eyes. based on the pediatricians sample, how many babies born in allegheny county would you expect to have blue eyes?
remember:
$p(event)=\frac{number\\ of\\ favorable\\ outcomes}{number\\ of\\ possible\\ outcomes}$
a 9,330
b 3,240
c 2,500

Explanation:

Step1: Calculate the probability of a baby having blue eyes in the sample

The number of favorable outcomes (babies with blue eyes) is \(72\), and the number of possible outcomes (total babies in the sample) is \(288\).
Using the formula \(P(\text{blue eyes})=\frac{\text{number of favorable outcomes}}{\text{number of possible outcomes}}\), we have \(P(\text{blue eyes})=\frac{72}{288}=\frac{1}{4}\)

Step2: Use the probability to estimate the number of babies with blue eyes in the county

The total number of babies born in Allegheny County is \(12958\).
Let \(x\) be the number of babies with blue eyes. We know that \(P(\text{blue eyes})=\frac{x}{12958}\). Since \(P(\text{blue eyes}) = \frac{1}{4}\), we can set up the equation \(\frac{x}{12958}=\frac{1}{4}\), then \(x=\frac{12958}{4}=3239.5\approx3240\)

Answer:

B. \(3,240\)