Probability of Picking a Black Ball: A Simple Guide

This article will provide a detailed explanation of how to calculate the probability of picking a black ball from a bag containing different colored balls. Understanding this concept is crucial for those interested in basic probability and random selection.

Basic Setup

Imagine you have a bag with the following distribution of balls:

6 white balls 8 blue balls 4 black balls 2 red balls

If you were to pick one ball at random, how would you find the probability of it being black?

Step-by-Step Solution

The first step in solving this problem is to determine the total number of balls in the bag:

Total number of balls 6 white 8 blue 4 black 2 red 20 balls

Direct Calculation Method

The probability of picking a black ball is calculated as follows:

Probability of picking a black ball Number of black balls / Total number of balls

* 4 black balls / 20 total balls 1/5 or 20%*

Expressed as a decimal: 0.20, or as a fraction: 1/5.

Inverse Calculation Method

Another method to approach this problem is to consider the probability of not picking a black ball, which is the same as picking a white, blue, or red ball:

Probability of not picking a black ball Number of non-black balls / Total number of balls

* (6 white 8 blue 2 red) / 20 total balls 16/20 4/5*

Therefore, the probability of picking a black ball is:

Probability of picking a black ball 1 - Probability of not picking a black ball

* 1 - 4/5 1/5 or 20%*

Collaborative Examples

Let's work through a few more examples:

Example 1: If there are 7 white balls, 3 red balls, and 2 black balls in a bag, what is the probability of picking a black ball?

Total number of balls 7 white 3 red 2 black 12 balls Probability of picking a black ball 2 black / 12 total balls 1/6 or 16.67%

Example 2: In another scenario, there are 534 balls in a bag, with 12 of them being of a certain color, primarily 3 red balls. What is the probability of picking a red ball?

Probability of picking a red ball 3 red / 534 total balls 1/178 or approximately 0.56%

Example 3: In a situation where the distribution of balls is as follows:

White balls 8 Red balls 5 Black balls 4

What is the probability of picking a white or black ball?

Total number of balls 8 white 5 red 4 black 17 balls Probability of picking a white or black ball 12 / 17 or approximately 70.59%

Frequently Asked Questions

Here are some common questions about probabilities:

Q: What is the probability of picking a black ball?
A: The probability of picking a black ball is 1/5 or 20%. Q: How do you find the probability of not picking a black ball?
A: The probability of not picking a black ball is 4/5 or 80%. Q: Is the probability of picking a white or black ball higher or lower than picking a red ball?
A: The probability of picking a white or black ball is 12/17, which is 2.4 times higher than the probability of picking a red ball, which is 5/17.

With a clear understanding of these concepts, you can easily calculate probabilities for various scenarios involving random selection. Whether you're studying for a math exam, or simply curious about basic probability, these techniques will serve you well.