One of the most profitable items at Al's Auto Security Shop is the remote starting system. Let x be the number of such systems installed on a given day at this shop. The following table lists the frequency distribution of x for the past 80 days. x 1 2 3 4 5 f 8 20 24 16 12 a. Construct a probability distribution table for the number of remote starting systems installed on a given day. x P(x) 1 Enter you answer; P(1) 2 Enter you answer; P(2) 3 Enter you answer; P(3) 4 Enter you answer; P(4) 5 Enter you answer; P(5) c. Find the following probabilities. i. P(x=5) P(x=5)= Enter you answer in accordance to the item i) of the question statement ii. P(x≥2) P(x≥2)= Enter you answer in accordance to the item ii) of the question statement iii. P(2≤x≤4) P(2≤x≤4)= Enter you answer in accordance to the item iii) of the question statement iv. P(x<4) P(x<4)= Enter you answer in accordance to the item iv) of the question statement
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.
| x | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| f | 8 | 20 | 24 | 16 | 12 |
a. Construct a probability distribution table for the number of remote starting systems installed on a given day.
| x | P(x) |
|---|---|
| 1 | Enter you answer; P(1) |
| 2 | Enter you answer; P(2) |
| 3 | Enter you answer; P(3) |
| 4 | Enter you answer; P(4) |
| 5 | Enter you answer; P(5) |
c. Find the following probabilities.
i. P(x=5)
P(x=5)= Enter you answer in accordance to the item i) of the question statement
ii. P(x≥2)
P(x≥2)= Enter you answer in accordance to the item ii) of the question statement
iii. P(2≤x≤4)
P(2≤x≤4)= Enter you answer in accordance to the item iii) of the question statement
iv. P(x<4)
P(x<4)= Enter you answer in accordance to the item iv) of the question statement
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