You roll two fair dice, a green one and a red one. Are the outcomes on the dice independent? What is the probability of 5 on the green die and 3 on the red die? Find the probability of 3 on both die?
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.
- You roll two fair dice, a green one and a red one.
- Are the outcomes on the dice independent?
- What is the
probability of 5 on the green die and 3 on the red die? - Find the probability of 3 on both die?
- Find the probability of [(5 on green die and 3 on red die) or (3 on a green die and 5 on the red die).]
- What is the probability of getting a sum of 4?
- What is the probability of getting a sum of 8?
- What is the probability of getting a sum or either 4 or 8?
Since you have posted a question with multiple sub-parts, we will solve first three subparts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved
Rolling two dices are an independent event as outcome of one die does not depend upon the outcomes of another die that is probability of outcomes of green die does not change the probability of outcome of red die.
For example: define following events
A: obtaining 1 on green die
B: Obtaining 2 on red die
A and B :obtaining 1 on green die and Obtaining 2 on red die
The probabilities of above events can be calculated as:
Thus the outcomes on the dice independent?
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
