One ball is drawn at random from a bag containing 4 red balls and 8 white balls. (Enter your probabilities as fractions.) (a) What is the probability that the ball is red? (b) What is the probability that the ball green? (c) What is the probability that the ball is red or white?
Compound Probability
Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent.
Tree diagram
Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described.
Conditional Probability
By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.
![**Probability Exercise: Drawing Balls from a Bag**
In this exercise, we consider a scenario where one ball is drawn at random from a bag. The bag contains a total of 12 balls: 4 red balls and 8 white balls. You will calculate probabilities based on these conditions and provide your answers as fractions.
### Questions:
(a) **What is the probability that the ball is red?**
- Calculate the likelihood of drawing a red ball from the bag.
(b) **What is the probability that the ball is green?**
- Determine the probability of drawing a green ball, if any exist.
(c) **What is the probability that the ball is red or white?**
- Assess the probability of drawing either a red or a white ball.
Use these questions to enhance your understanding of basic probability concepts. Consider the total number of balls in the bag when deriving your fractions for each answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8533e211-c3b0-4c2c-a0a5-c3ff9e21dbc2%2F88b5155b-7554-424c-81cc-caff8a0f0cae%2Fakh2d5b_processed.png&w=3840&q=75)
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