Question

A golf ball is selected at random from a container. If the container has 9 white balls, 8 green balls, and 3 orange balls, find the probability of each event. The golf ball is white or orange.

Short answer

The probability is \(\frac{3}{5}\).

Step-by-step solution

Calculate the total number of golf balls

Add the number of white, green, and orange golf balls together. We have 9 white balls, 8 green balls, and 3 orange balls.Total number of balls = 9 + 8 + 3

Simplify the total

Simplify the total number of golf balls.Total number of balls = 20

Calculate the number of favorable outcomes

Identify the number of white or orange golf balls. Sum the number of white and orange balls.Number of white balls = 9Number of orange balls = 3Number of favorable outcomes = 9 + 3

Simplify the number of favorable outcomes

Simplify the number of favorable outcomes.Number of favorable outcomes = 12

Calculate the probability

Divide the number of favorable outcomes by the total number of golf balls.Probability = \(\frac{12}{20}\)

Simplify the probability

Simplify the fraction to its lowest terms.Probability = \(\frac{3}{5}\)

Key concepts

favorable outcomes

In probability, a favorable outcome is an outcome that satisfies the condition specified in the problem.
For our exercise, favorable outcomes are the events where the selected golf ball is either white or orange.
Identifying and counting favorable outcomes is a crucial step. In this exercise, there are 9 white balls and 3 orange balls. So, the total number of favorable outcomes is 9 + 3 = 12.
It's important to remember that all favorable outcomes must align exactly with the condition given in the problem.

total outcomes

Total outcomes represent all possible results of the experiment.
In this exercise, the total outcome is the number of every golf ball within the container.
We get the total by simply adding up all the golf balls: 9 white, 8 green, and 3 orange, which sums up to 20.
Knowing the total number of outcomes is crucial because it forms the denominator of our probability fraction.

simplifying fractions

Simplifying fractions makes our probabilities easier to understand and neat.
In our exercise, after calculating the fraction \(\frac{12}{20}\), we simplify it to its lowest terms.
We find the greatest common divisor (GCD) of the numerator and the denominator. For 12 and 20, the GCD is 4.
So, we divide both the numerator and the denominator by 4: \(\frac{12 \div 4}{20 \div 4} = \frac{3}{5}\).
This gives us the simplified probability of \(\frac{3}{5}\). Simplifying fractions not only makes our results more precise but also eliminates common mistakes.

golf ball probability

Calculating the probability of picking a golf ball is a straightforward process once we understand the basic concepts.
In the given exercise, we determine the probability by using the formula: Probability = \(\frac{Number \text{ of favorable outcomes}}{Total \text{ number of outcomes}}\).
Here, we plug in our values: \(\frac{12}{20}\).
To further express this probability in its simplest form, we simplify it to \(\frac{3}{5}\).
This fraction tells us that there is a \(\frac{3}{5}\) chance to randomly pick either a white or orange golf ball from the container.

random selection

Random selection means every item in the set has an equal chance of being chosen.
In our exercise, every golf ball in the container has an equal chance of being picked.
This concept is fundamental in probability because it guarantees that our outcomes are fair and unbiased.
By ensuring a random selection, we can correctly apply our probability calculations to predict the chances of different events.
Random selection is vital in many probability-related experiments, as it lays the groundwork for accurate results.