Question

the two - way frequency table shows the current inventory of hardwood that a lumberyard carries. suppose a customer randomly selects a board from the lumberyards inventory. use the table to calculate each probability. round to the nearest tenth of a percent if necessary. sample problem p(oak) $\frac{62}{210}approx0.295 = 29.5%$ p(cherry or 1×4)

Explanation:

Step1: Recall probability formula

The formula for the probability of an event \(A\) or \(B\) is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Here, \(A\) is the event of selecting cherry - wood and \(B\) is the event of selecting a \(1\times4\) board.

Step2: Calculate \(P(\text{cherry})\)

The total number of boards is \(n = 210\). The number of cherry - wood boards is \(n(\text{cherry})=78\). So \(P(\text{cherry})=\frac{78}{210}\).

Step3: Calculate \(P(1\times4)\)

The number of \(1\times4\) boards is \(n(1\times4)=54\). So \(P(1\times4)=\frac{54}{210}\).

Step4: Calculate \(P(\text{cherry and }1\times4)\)

The number of cherry \(1\times4\) boards is \(n(\text{cherry and }1\times4)=28\). So \(P(\text{cherry and }1\times4)=\frac{28}{210}\).

Step5: Calculate \(P(\text{cherry or }1\times4)\)

\[

$$\begin{align*} P(\text{cherry or }1\times4)&=P(\text{cherry})+P(1\times4)-P(\text{cherry and }1\times4)\\ &=\frac{78}{210}+\frac{54}{210}-\frac{28}{210}\\ &=\frac{78 + 54-28}{210}\\ &=\frac{104}{210}\approx0.495 \end{align*}$$

\]

Step6: Convert to percentage

To convert the decimal to a percentage, multiply by 100. So \(0.495\times100 = 49.5\%\)

Answer:

49.5%