Problem 60 - Algebra and Trigonometry

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 not green.

Step-by-Step Solution

Answer

The probability is 0.6.

Step 1: Identify total number of golf balls

First, find the total number of golf balls in the container. There are 9 white balls, 8 green balls, and 3 orange balls. Add these numbers together to get the total: \[ 9 + 8 + 3 = 20 \] So, there are 20 golf balls in total.

Step 2: Determine the number of non-green golf balls

Next, find the number of golf balls that are not green. There are 9 white balls and 3 orange balls. Add these numbers together: \[ 9 + 3 = 12 \] So, there are 12 non-green golf balls.

Step 3: Calculate the probability

Now, determine the probability that a randomly selected golf ball is not green. Probability is found by dividing the number of favorable outcomes by the total number of outcomes. Hence, the probability is: \[ P(\text{Not Green}) = \frac{12}{20} = \frac{3}{5} = 0.6 \]

Key Concepts

Probability Calculation

Probability is a concept used to measure the likelihood of an event happening. We calculate it by dividing the number of favorable outcomes by the total number of possible outcomes.
Let's break it down further:

• **Favorable Outcomes:** These are the results we are interested in. In this case, it's the number of golf balls that are **not green**.
  
• **Total Outcomes:** This is the total number of golf balls available in the container.

For example, if you have a container with several golf balls and you want to calculate the probability of picking a non-green ball, you first count the total number of golf balls and then count how many of them are non-green. If we have a total of 20 golf balls and 12 of them are non-green, the probability is: \ \[ P(\text{Not Green}) = \frac{12}{20} = 0.6 \ \]

Non-Green Golf Balls

The problem asks for the probability of selecting a non-green golf ball. To achieve this, we need to determine how many golf balls are not green.
Given the container has:

• 9 white golf balls
• 8 green golf balls
• 3 orange golf balls

The non-green golf balls are the white and orange ones. To find the number of non-green balls, we sum the white and orange balls: \ \[ 9 + 3 = 12 \ \]
Thus, there are 12 non-green golf balls. This step is crucial because it defines the favorable outcomes we use in our probability calculation.

Random Selection

Random selection means that every item has an equal chance of being chosen. In the context of our problem, it means each golf ball has the same chance of being picked.
Random selection ensures fairness and unpredictability.
When applied to our scenario:

• There are 20 total golf balls.
• Each ball has a 1 in 20 chance of being selected.

The random nature is essential to calculating the probability. If the selection weren't random, the likelihood of picking a specific ball might not be even. Hence, for the probability calculations to be accurate, the random selection assumption is vital.
In our case, following this principle, the probability that a randomly chosen ball is not green is confidently calculated.