A Bag Contains 10 Red Marbles, 15 Yellow Marbles, 5 Green Marbles, And 20 Blue Marbles. Two Marbles Are Drawn From The Bag.Which Expression Represents The Probability That One Of The Marbles Is Red And The Other Is Blue?A. [$\frac{{30 P_2}}{{50
**A Bag of Marbles: Understanding Probability**
What is the Problem?
A bag contains 10 red marbles, 15 yellow marbles, 5 green marbles, and 20 blue marbles. Two marbles are drawn from the bag. We need to find the probability that one of the marbles is red and the other is blue.
Understanding the Problem
To solve this problem, we need to understand the concept of probability. Probability is a measure of the likelihood of an event occurring. In this case, the event is drawing one red marble and one blue marble from the bag.
The Total Number of Marbles
The total number of marbles in the bag is 10 (red) + 15 (yellow) + 5 (green) + 20 (blue) = 50 marbles.
Drawing Two Marbles
When we draw two marbles from the bag, the total number of possible outcomes is the number of ways we can choose 2 marbles from 50. This can be calculated using the combination formula:
50C2 = 50! / (2! * (50-2)!) = 50! / (2! * 48!) = (50 * 49) / 2 = 1225
The Favorable Outcomes
The favorable outcomes are the outcomes where we draw one red marble and one blue marble. There are two ways this can happen:
- We draw a red marble first and then a blue marble.
- We draw a blue marble first and then a red marble.
The number of ways to draw a red marble first and then a blue marble is 10C1 * 20C1 = 10 * 20 = 200.
The number of ways to draw a blue marble first and then a red marble is 20C1 * 10C1 = 20 * 10 = 200.
The total number of favorable outcomes is 200 + 200 = 400.
The Probability
The probability of drawing one red marble and one blue marble is the number of favorable outcomes divided by the total number of possible outcomes:
P = 400 / 1225
Simplifying the Fraction
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 5:
P = (400 / 5) / (1225 / 5) = 80 / 245
The Final Answer
The final answer is 80/245.
Q&A
Q: What is the probability of drawing one red marble and one blue marble from the bag?
A: The probability of drawing one red marble and one blue marble from the bag is 80/245.
Q: How many marbles are in the bag?
A: There are 50 marbles in the bag.
Q: How many ways can we draw two marbles from the bag?
A: There are 1225 ways to draw two marbles from the bag.
Q: What are the favorable outcomes?
A: The favorable outcomes are the outcomes where we draw one red marble and one blue marble.
Q: How many ways can we draw one red marble and one blue marble?
A: There are 400 ways to draw one red marble and one blue marble.
Q: What is the probability of drawing one red marble and one blue marble?
A: The probability of drawing one red marble and one blue marble is 80/245.
Q: Can we simplify the fraction?
A: Yes, we can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 5.
Q: What is the final answer?
A: The final answer is 80/245.