5-103. An international charity builds homes for disaster victims. Often the materials are donated. The charity recently built 45 homes. \( 20 \% \) of the houses havere granite for the kitchen countertops while the rest have porcelain tile. Fife the homes have red oak for the wooden kitchen floor, 20 have white oak, an ten have maple. If a disaster victim is randomly assigned to a home, What is probability (in percent) of getting a home with an oak floor and granite countertops?

To find the probability of getting a home with both oak flooring and granite countertops, we first need to determine how many homes meet both criteria. Out of the 45 homes, \(20\%\) have granite countertops, so: \[ 0.2 \times 45 = 9 \text{ homes with granite countertops.} \] For the oak flooring, there are 5 homes with red oak, 20 homes with white oak, and 10 homes with maple. This gives us: \[ 5 + 20 = 25 \text{ homes with an oak floor.} \] Now, we need to find the homes with both granite countertops and oak flooring. Assuming that the choice of flooring and countertops is independent (which is a commonly used assumption in probability problems unless stated otherwise), we can calculate the probability of selecting a home that meets both conditions. The total number of homes is 45. The probability of getting a home with oak flooring and granite countertops is the product of the probabilities of each event: \[ P(\text{oak floor}) = \frac{25}{45} \] and \[ P(\text{granite countertops}) = \frac{9}{45}. \] Calculating this gives: \[ P(\text{oak floor and granite countertops}) = \left(\frac{25}{45}\right) \times \left(\frac{9}{45}\right) = \frac{225}{2025} = \frac{1}{9}. \] Thus, the probability in percent is: \[ \frac{1}{9} \approx 0.1111, \] or \[ 0.1111 \times 100 \approx 11.11\%. \] So, the probability of getting a home with an oak floor and granite countertops is approximately **11.11%**.