Question

A vase has 4 yellow flowers, 4 red flowers, and 8 blue flowers. Donna took a flower and gave it to her mom, and then took another and gave it to her sister. What is the probability that the first flower was red and the second flower was blue?answer choices: 2/15 1/6 1/8 1/32

Answer 1

Let's begin by listing out the given information

Total number of flowers = 4 + 4 + 8 = 16

Yellow = 4 flowers

Red = 4 flowers

Blue = 8 flowers

The probability that the first flower was red is:

$\begin{gathered} P(red)=\frac{No.of.red.flower}{Total.no.of.flowers} \\ P(red)=\frac{4}{16}=\frac{1}{4} \\ P(red)=\frac{1}{4} \end{gathered}$

After removing the first flower (red), the probability that the second flower was blue is:

$\begin{gathered} P(blue)=\frac{No.of.blue.flower}{Total.no.of.flowers} \\ Total.no.of.flowers.left=16-1=15 \\ P(blue)=\frac{8}{15} \end{gathered}$

The total probability for this event is given by the product of P(red) & P(blue):

$\begin{gathered} P(total)=P(red)\cdot P(blue) \\ P(total)=\frac{1}{4}\cdot\frac{8}{15}=\frac{1\cdot8}{4\cdot15} \\ P(total)=\frac{8}{60}=\frac{2}{15} \\ P(total)=\frac{2}{15} \end{gathered}$

Hence, 2/15 is the answer