Question

lisa 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. 0.25 0.13 0.09 0.32

Explanation:

Step1: Calculate the total number of marbles

The total number of marbles is \(4 + 6+12=22\).

Step2: Calculate the probability of pulling a red marble first

The probability of pulling a red marble first is \(P(\text{red})=\frac{4}{22}\).

Step3: Calculate the number of marbles left after pulling a red marble

After pulling a red marble, the number of marbles left is \(22 - 1=21\).

Step4: Calculate the probability of pulling a yellow marble second

The probability of pulling a yellow marble second is \(P(\text{yellow})=\frac{12}{21}\).

Step5: Calculate the combined probability

Since these are independent - events (the first draw affects the second draw as there is no replacement), the combined probability \(P = P(\text{red})\times P(\text{yellow})\).

$$P=\frac{4}{22}\times\frac{12}{21}=\frac{48}{462}\approx0.104\approx0.10$$

Answer:

\(0.10\)