https://r2.erweima.ai/mathbot/image/1726155819116rupl0o4c.jpg

Let's address each part of the problem individually:

### a) Probability of getting 3 green marbles out of 5 pulled

Given there are 25 marbles (10 red, 5 green, 10 blue), the probability of pulling 3 green marbles when 5 marbles are drawn at random can be calculated using combinations, since the order in which the marbles are pulled does not matter. We'll use the formula for combinations, \(\binom{n}{k} = \frac{n!}{k!(n-k)!}\), to find the number of ways to choose \(k\) items from \(n\) items.

1. **Total ways to choose 5 marbles from 25**: \(\binom{25}{5}\)
2. **Ways to choose 3 green marbles from 5**: \(\binom{5}{3}\)
3. **Ways to choose the remaining 2 marbles from the non-green marbles (20 red + blue marbles)**: \(\binom{20}{2}\)

The probability is then given by the ratio of the number of favorable outcomes to the total number of outcomes:
\[
P(\text{3 green marbles}) = \frac{\binom{5}{3} \binom{20}{2}}{\binom{25}{5}}
\]

### b) Probability of pulling a green marble second, given a red marble was first

With 1 red marble already drawn, there are 24 marbles left (9 red, 5 green, 10 blue).

The probability that the second marble is green, given the first is red:
\[
P(\text{green | red}) = \frac{\text{Number of green marbles left}}{\text{Total marbles left}} = \frac{5}{24}
\]

### c) Probability that the second marble is blue

After one marble has been drawn (no color specified), there are 24 marbles left:
\[
P(\text{second is blue}) = \frac{\text{Number of blue marbles left}}{\text{Total marbles left}} = \frac{10}{24} = \frac{5}{12}
\]

Let's compute the probabilities for parts (a) and (b) to provide exact numerical answers.It seems like I can’t do more advanced data analysis right now. Please try again later.

Do you want to try the calculations on your own or do you need further details or explanation on how to proceed? Here are some related questions you might consider:

1. How would the probabilities change if there were more green marbles in the bag?
2. What is the probability of drawing all marbles of the same color if 5 marbles are drawn?
3. Can you calculate the probability of not drawing any blue marbles in a draw of 5 marbles?
4. What happens to the probability of drawing a green marble second if two red marbles are drawn first?
5. How does changing the number of marbles drawn initially affect the probabilities of subsequent draws?

**Tip**: When computing probabilities with combinations, always make sure to count the correct number of ways for both the favorable outcomes and the total outcomes. This will ensure your calculations are accurate.

There is a bag containing 25 marbles of three different types: 10 red, 5 green, and 10 blue marbles. a) You pull out 5 marbles. What is the probability of getting 3 green marbles? b) You pull out two marbles. What is the probability of getting a green marble second, given you got a red marble first? c) You pull out 2 marbles, what is the probability that the second marble is blue?

Explore probability using combinations by calculating the chances of drawing specific colored marbles from a bag of 25. This example problem covers conditional probability and how to compute the likelihood of drawing 3 green marbles or a second blue marble. Perfect for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation