A Bag Contains 11 Brown, 16 Black, 19 Gray, And 9 White Pebbles. You Pick One Pebble At Random. Find The Probability That It Is Not Black.${ P(\text{not Black}) = , ? }$Simplify Your Answer Completely.
Introduction
In this article, we will explore the concept of probability and how it can be used to determine the likelihood of an event occurring. We will use a real-world example to illustrate this concept, where we have a bag containing 11 brown, 16 black, 19 gray, and 9 white pebbles. Our goal is to find the probability of picking a pebble that is not black.
Understanding Probability
Probability is a measure of the likelihood of an event occurring. It is usually expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. In this case, we want to find the probability of picking a pebble that is not black.
Calculating the Probability
To calculate the probability of picking a pebble that is not black, we need to first find the total number of pebbles in the bag. We can do this by adding up the number of brown, black, gray, and white pebbles.
Total number of pebbles = 11 (brown) + 16 (black) + 19 (gray) + 9 (white)
Total number of pebbles = 55
Next, we need to find the number of pebbles that are not black. We can do this by subtracting the number of black pebbles from the total number of pebbles.
Number of pebbles that are not black = Total number of pebbles - Number of black pebbles
Number of pebbles that are not black = 55 - 16
Number of pebbles that are not black = 39
Now that we have the number of pebbles that are not black, we can calculate the probability of picking a pebble that is not black. We can do this by dividing the number of pebbles that are not black by the total number of pebbles.
Probability of picking a pebble that is not black = Number of pebbles that are not black / Total number of pebbles
Probability of picking a pebble that is not black = 39 / 55
Simplifying the Answer
To simplify the answer, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 39 and 55 is 1.
Probability of picking a pebble that is not black = 39 / 55
Probability of picking a pebble that is not black = 39 / (5 * 11)
Probability of picking a pebble that is not black = 3 / 5
Conclusion
In conclusion, the probability of picking a pebble that is not black from a bag containing 11 brown, 16 black, 19 gray, and 9 white pebbles is 3/5 or 60%.
Real-World Applications
The concept of probability is used in many real-world applications, such as:
- Insurance: Insurance companies use probability to determine the likelihood of an event occurring, such as a car accident or a natural disaster.
- Finance: Financial institutions use probability to determine the likelihood of a stock or bond performing well.
- Medicine: Medical professionals use probability to determine the likelihood of a patient responding to a treatment.
- Engineering: Engineers use probability to determine the likelihood of a system or component failing.
Final Thoughts
Introduction
In our previous article, we explored the concept of probability and how it can be used to determine the likelihood of an event occurring. We used a real-world example to illustrate this concept, where we had a bag containing 11 brown, 16 black, 19 gray, and 9 white pebbles. Our goal was to find the probability of picking a pebble that is not black. In this article, we will answer some frequently asked questions related to this topic.
Q: What is the probability of picking a black pebble?
A: To find the probability of picking a black pebble, we need to divide the number of black pebbles by the total number of pebbles.
Probability of picking a black pebble = Number of black pebbles / Total number of pebbles
Probability of picking a black pebble = 16 / 55
Probability of picking a black pebble = 8 / 11
Q: What is the probability of picking a non-black pebble?
A: We already calculated this in our previous article. The probability of picking a non-black pebble is 3/5 or 60%.
Q: What is the probability of picking a brown pebble?
A: To find the probability of picking a brown pebble, we need to divide the number of brown pebbles by the total number of pebbles.
Probability of picking a brown pebble = Number of brown pebbles / Total number of pebbles
Probability of picking a brown pebble = 11 / 55
Probability of picking a brown pebble = 1 / 5
Q: What is the probability of picking a gray pebble?
A: To find the probability of picking a gray pebble, we need to divide the number of gray pebbles by the total number of pebbles.
Probability of picking a gray pebble = Number of gray pebbles / Total number of pebbles
Probability of picking a gray pebble = 19 / 55
Probability of picking a gray pebble = 19 / (5 * 11)
Probability of picking a gray pebble = 19 / 55
Q: What is the probability of picking a white pebble?
A: To find the probability of picking a white pebble, we need to divide the number of white pebbles by the total number of pebbles.
Probability of picking a white pebble = Number of white pebbles / Total number of pebbles
Probability of picking a white pebble = 9 / 55
Probability of picking a white pebble = 9 / (5 * 11)
Probability of picking a white pebble = 9 / 55
Q: Can I use a calculator to find the probability?
A: Yes, you can use a calculator to find the probability. Simply enter the number of pebbles that are not black and the total number of pebbles, and the calculator will give you the probability.
Q: Can I use a probability formula to find the probability?
A: Yes, you can use a probability formula to find the probability. The formula is:
P(A) = Number of favorable outcomes / Total number of outcomes
In this case, the number of favorable outcomes is the number of pebbles that are not black, and the total number of outcomes is the total number of pebbles.
Conclusion
In this article, we answered some frequently asked questions related to the probability of picking a pebble that is not black. We calculated the probability of picking a black pebble, a non-black pebble, a brown pebble, a gray pebble, and a white pebble. We also discussed how to use a calculator and a probability formula to find the probability.