Liz has a bag containing 15 counters. The table below shows the number of counters of each color in the bag. As a part of a probability experiment for science club, Liz randomly picks a counter from the bag then replaces it. She repeats this 450 times.
| Counter Colors | Number of Counters In The Bag |
| -------------- | ------------------------------ |
| White | 3 |
| Red | 8 |
| Blue | 3 |
| Black | 1 |
Liz randomly picks a counter out of the bag. What is the probability that it will be red?
Part A
Show your work and explain your answer.
Part B
Predict the number of times out of 450 Liz will pick a red counter.
Answer (1)
Calculate the probability of picking a red counter: 15 8 .
Multiply the probability by the number of trials (450) to predict the number of times a red counter will be picked.
15 8 × 450 = 240 .
Liz is predicted to pick a red counter 240 times.
Explanation
Understanding the Problem Let's break down this probability problem step by step! First, we need to figure out the chance of Liz picking a red counter. Then, we'll use that probability to predict how many times she'll pick a red counter if she does the experiment 450 times.
Calculating the Probability of Picking a Red Counter To find the probability of picking a red counter, we need to compare the number of red counters to the total number of counters in the bag. There are 8 red counters, and a total of 15 counters. So, the probability of picking a red counter is: P ( re d ) = Total number of counters Number of red counters = 15 8 This means that for any single pick, Liz has an 8 out of 15 chance of picking a red counter.
Predicting the Number of Times Liz Picks a Red Counter Now, let's predict how many times Liz will pick a red counter if she repeats the experiment 450 times. To do this, we multiply the probability of picking a red counter by the number of times she repeats the experiment: Predicted number of red counters = P ( re d ) × Number of trials = 15 8 × 450 Predicted number of red counters = 0.5333 × 450 = 240 So, we predict that Liz will pick a red counter 240 times out of 450.
Final Answer So, the probability that Liz will pick a red counter is 15 8 , and we predict she will pick a red counter 240 times out of 450.
Examples
Imagine you're running a game at a school fair where kids randomly pick colored tokens from a bag to win prizes. If you know the probability of picking a winning color (like red), you can predict how many prizes you'll likely give out if 450 kids play the game. This helps you plan how many prizes to have on hand! The calculation we did is similar to figuring out how many winners to expect: we found the probability of picking red, and then multiplied it by the number of players to estimate the number of winners.
