Problem 57 - 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 white or green.

Step-by-Step Solution

Answer

\( \frac{17}{20} \)

Step 1: Determine the total number of balls

Add up all the balls in the container. There are 9 white balls, 8 green balls, and 3 orange balls. Therefore, the total number of balls is: \[ 9 + 8 + 3 = 20 \]

Step 2: Calculate the number of favorable outcomes

Find the number of balls that are either white or green. This includes all the white and green balls. \[ 9 + 8 = 17 \]

Step 3: Calculate the probability

The probability of selecting a white or green ball is the number of white or green balls divided by the total number of balls. \[ \frac{17}{20} \]

Key Concepts

Random Selection

In probability, 'random selection' refers to choosing an item without any bias or predictable pattern. In our example, we have a container with golf balls of different colors. Each time you pick a ball, you should not favor any color over another. This ensures every ball has an equal chance of being selected. Random selection is essential to achieve impartial results in probability calculations.

Favorable Outcomes

Favorable outcomes are the outcomes that match the event we are interested in. For this exercise, our events of interest are choosing either a white or green ball. We need to count all the white and green balls in the container. There are 9 white balls and 8 green balls, totaling \(9 + 8 = 17\). These 17 balls are the favorable outcomes for our event.

Total Outcomes

Total outcomes are all possible results from a random selection. For our problem, the total number of outcomes is the sum of all balls in the container. We add up the white, green, and orange balls: \(9 + 8 + 3 = 20\). This total indicates the number of possibilities we have when picking a ball from the container.

Addition Rule

The addition rule in probability helps us find the probability of one event or another happening. Since we are looking for the probability of selecting a white or green ball, we add the probabilities of picking each type of ball. Given the number of favorable outcomes (17) and the total outcomes (20), we calculate the probability: \(\frac{17}{20}\). This means the probability of picking a white or green ball is 0.85 or 85%.