Question

a box of matching game pieces contains 8 red pieces, 5 green pieces, and 7 yellow pieces. you reach in and randomly take out one piece and then a second piece. find the probability of drawing a green piece followed by a red piece.
(1 point)
$\frac{2}{19}$
$\frac{1}{10}$
$\frac{10}{39}$
$\frac{7}{76}$

Explanation:

Step1: Calculate total number of pieces

Total pieces = \(8 + 5+7=20\)

Step2: Calculate probability of first - draw (green)

Probability of drawing green first, \(P(G)=\frac{5}{20}\)

Step3: Calculate probability of second - draw (red)

After drawing a green piece, total pieces left = \(19\), red pieces = \(8\). Probability of drawing red second, \(P(R|G)=\frac{8}{19}\)

Step4: Use multiplication rule for dependent events

By \(P(G\cap R)=P(G)\times P(R|G)\), we have \(P(G\cap R)=\frac{5}{20}\times\frac{8}{19}=\frac{40}{380}=\frac{1}{10}\)

Answer:

\(\frac{1}{10}\) (corresponding to the second option)