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 lumberyard’s inventory. use the table to calculate each probability. round to the nearest tenth of a percent if necessary.

	size
type of hardwood	oak	20	13	17	12	62
	maple	14	28	9	19	70
	cherry	8	17	28	25	78
	total	42	58	54	56	210

sample problem
$p(oak)$
$\frac{62}{210}approx0.295 = 29.5%$

$p(maple or 1\times6)$

enter the answer in the space provided. use numbers instead of words.

question 1 of 1

Explanation:

Step1: Recall probability formula for or - events

$P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)$

Step2: Calculate $P(\text{maple})$

The total number of hardwood boards is $210$. The number of maple boards is $70$. So $P(\text{maple})=\frac{70}{210}$.

Step3: Calculate $P(1\times6)$

The number of $1\times6$ boards is $56$. So $P(1\times6)=\frac{56}{210}$.

Step4: Calculate $P(\text{maple and }1\times6)$

The number of maple $1\times6$ boards is $19$. So $P(\text{maple and }1\times6)=\frac{19}{210}$.

Step5: Calculate $P(\text{maple or }1\times6)$

$P(\text{maple or }1\times6)=\frac{70}{210}+\frac{56}{210}-\frac{19}{210}=\frac{70 + 56-19}{210}=\frac{107}{210}\approx0.5095$
Converting to percentage: $0.5095\times100 = 51.0\%$ (rounded to the nearest tenth of a percent)

Answer:

$51.0$