Question

lola pulls two marbles from a bag containing four red marbles, four blue marbles, and 12 yellow marbles without replacing them.
what is the probability that she pulled out a red marble first and a yellow marble second? express your answer in decimal form, rounded to the nearest hundredth.
0.09
0.13
0.25
0.32

Explanation:

Step1: Calculate total number of marbles

Total marbles = \(4 + 4+12=20\)
Probability of first - marble (red): \(P(R_1)=\frac{4}{20}\)

Step2: Calculate probability of second - marble (yellow)

After pulling a red marble, number of marbles left \(= 19\)
Probability of second - marble (yellow): \(P(Y_2)=\frac{12}{19}\)

Step3: Calculate combined probability

Using the multiplication rule for dependent events \(P = P(R_1)\times P(Y_2)\)
\(P=\frac{4}{20}\times\frac{12}{19}=\frac{48}{380}\approx0.13\)

Answer:

0.13