Suppose that a finite class contains 60%60% freshmen, 20%20% sophomores, 10%10% juniors, and the rest seniors. Suppose that 20%20% freshmen, 40%40% sophomores, 60%60% juniors, and 70%70% of seniors pass the class. Answer the following questions: 1. Given that the student is a sophomore, what is the probability that she fails the class? 2. What is the probability that a randomly selected student passes the class? 3.What is the probability that a randomly selected student is a senior that passes the class?
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.
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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.
Suppose that a finite class contains 60%60% freshmen, 20%20% sophomores, 10%10% juniors, and the rest seniors. Suppose that 20%20% freshmen, 40%40% sophomores, 60%60% juniors, and 70%70% of seniors pass the class. Answer the following questions:
1. Given that the student is a sophomore, what is the probability that she fails the class?
2. What is the probability that a randomly selected student passes the class?
3.What is the probability that a randomly selected student is a senior that passes the class?
Given information
Class contains 60% freshmen
20 % sophomore
10% juniors
10% seniors
20% freshmen pass
40% sophomores pass
50% juniors pass
70% seniors pass
All the information is shown in the table
|
Pass |
Fail |
Total |
|
|
Freshmen |
0.60 x 0.20 = 0.12 |
0.60-0.12=0.48 |
0.60 |
|
Sophomore |
0.20 x 0.40 = 0.08 |
0.20 - 0.08 = 0.12 |
0.20 |
|
Junior |
0.10 x 0.50 = 0.05 |
0.10 - 0.05 = 0.05 |
0.10 |
|
Senior |
0.10 x 0.70 = 0.07 |
0.10 - 0.07 = 0.03 |
0.10 |
|
Total |
0.32 |
0.68 |
1.00 |
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