In a class of students, the following data table summarizes how many students have a brother or a sister. What is the probability that a student has a brother given that they have a sister? Has a brother Does not have a brother 11 Has a sister 4 Does not have a sister
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 and Sibling Relationships in a Class
In a class of students, the following data table summarizes how many students have a brother or a sister. The question posed is: What is the probability that a student has a brother given that they have a sister?
#### Data Table:
| | Has a Brother | Does Not Have a Brother |
|---------------------|---------------|-------------------------|
| Has a Sister | 4 | 11 |
| Does Not Have a Sister | 3 | 2 |
To find the probability that a student has a brother given that they have a sister, use the formula for conditional probability:
\[ P(\text{Brother}|\text{Sister}) = \frac{P(\text{Brother and Sister})}{P(\text{Sister})} \]
From the table, the number of students who have both a brother and a sister is 4. The total number of students who have a sister is \(4 + 11 = 15\).
Therefore, the probability is:
\[ P(\text{Brother}|\text{Sister}) = \frac{4}{15} \]
### Answer:
\[ \boxed{\frac{4}{15} \text{ or approximately } 0.267} \]
Submit your answer in the space provided below.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0fac6bec-f0b2-4056-963f-cf73547656d5%2F1925d545-879f-4304-a6d0-10bebda5dc3f%2Fn47hlsp_processed.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
