Question

a candle shop owner collected data on customers favorite scents, as shown in the table.
a customer is randomly selected. if the probabilities of a customer choosing floral and coconut as their favorite scents are the same, what is the value of the missing probabilities?
0.10
0.14
0.20
0.28

Explanation:

Step1: Sum of known probabilities

Sum the probabilities of lavender, vanilla, and cinnamon: \(0.31 + 0.18+0.23=\frac{31 + 18+23}{100}=\frac{72}{100} = 0.72\)

Step2: Let the probability of floral and coconut be \(x\) each

Since the sum of all probabilities is \(1\), we have the equation \(0.72+x + x=1\). Simplify it to \(0.72 + 2x=1\).

Step3: Solve for \(x\)

Subtract \(0.72\) from both sides: \(2x=1 - 0.72=0.28\). Then divide by \(2\): \(x=\frac{0.28}{2}=0.14\)

Answer:

\(0.14\) (the second option)