ms. florina buys a bag of different - colored rubber bands. she randomly selects a rubber band, records the…

ms. florina buys a bag of different - colored rubber bands. she randomly selects a rubber band, records the color, and returns it to the bag. she does this a total of 50 times and selects 8 red, 18 blue, 10 green, and 14 yellow rubber bands. based on this information, what is the probability that ms. florina will select a blue rubber band, return it to the bag, and then select a green rubber band? click the arrows to choose an answer from each menu. based on the given information, the probability that ms. florina will select a blue rubber band is choose... and the probability that she will select a green rubber band is choose... . the probability that she will select a blue rubber band, return it to the bag, and then select a green rubber band is choose... .

ms. florina buys a bag of different - colored rubber bands. she randomly selects a rubber band, records the color, and returns it to the bag. she does this a total of 50 times and selects 8 red, 18 blue, 10 green, and 14 yellow rubber bands. based on this information, what is the probability that ms. florina will select a blue rubber band, return it to the bag, and then select a green rubber band? click the arrows to choose an answer from each menu. based on the given information, the probability that ms. florina will select a blue rubber band is choose... and the probability that she will select a green rubber band is choose... . the probability that she will select a blue rubber band, return it to the bag, and then select a green rubber band is choose... .

Answer

Answer:

The probability that Ms. Florina will select a blue rubber band is $\frac{18}{50}=\frac{9}{25}$, the probability that she will select a green rubber band is $\frac{10}{50}=\frac{1}{5}$, and the probability that she will select a blue rubber band, return it to the bag, and then select a green rubber band is $\frac{9}{25}\times\frac{1}{5}=\frac{9}{125}$.

Explanation:

Step1: Calculate blue - band probability

The probability of an event is the number of favorable outcomes divided by the total number of outcomes. The total number of trials is $n = 50$, and the number of times a blue rubber band is selected is $18$. So the probability of selecting a blue rubber band $P(B)=\frac{18}{50}=\frac{9}{25}$.

Step2: Calculate green - band probability

The number of times a green rubber band is selected is $10$. So the probability of selecting a green rubber band $P(G)=\frac{10}{50}=\frac{1}{5}$.

Step3: Calculate combined probability

Since the selections are independent events (because the rubber band is returned to the bag), the probability of both events occurring is the product of their individual probabilities. So $P(B\text{ then }G)=P(B)\times P(G)=\frac{9}{25}\times\frac{1}{5}=\frac{9}{125}$.