Question

from a survey involving 1000 University students market research company found that 780 students on laptops 460 on cars and 380 owned cars and laptops if a university student is selected at random what is each empirical probability. (A) the student owns either a car or laptop. (B) the student owns neither a car nor a laptop is.

Answer 1

Considering the definition of probability:

• the probability that the student owns either a car or laptop is 86%.
• the probability that the student owns neither a car nor a laptop is 14%.

Definition of Probabitity

Probability is the greater or lesser possibility that a certain event will occur.

In other words, the probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.

The probability of any event A is defined as the quotient between the number of favorable cases (that is, the number of times that event A may or may not occur) and the total number of possible cases:

$Probability=\frac{number of favorable cases}{total number of possible cases}$

Union of events

The union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".

The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:

P(A∪B)= P(A) + P(B) -P(A∩B)

Complementary event

A complementary event, also called an opposite event, is made up of the inverse of the results of another event. That is, That is, given an event A, a complementary event is verified as long as the event A is not verified.

The probability of occurrence of the complementary event A' will be 1 minus the probability of occurrence of A:

P(A´)= 1- P(A)

Events and probability in this case

In first place, let's define the following events:

A: The event that a student owned a laptop.

B: The event that a student owned a car.

Then you know:

• P(A)= $\frac{780}{1000}$= 0.78
• P(B)= $\frac{460}{1000}$= 0.46
• P(F and R)= P(F∩R)= $\frac{380}{1000}$= 0.38 [The intersection of events, A∩B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A∩B is verified when A and B occur simultaneously.]

In this case, considering the definition of union of events, the probability that the student owns either a car or laptop is calculated as:

P(A∪B)= P(A) + P(B) -P(A∩B)

P(A∪B)= 0.78 + 0.46 -0.38

P(A∪B)= 0.86= 86%

Then, the probability that the student owns either a car or laptop is 86%.

On the other hand, considering the definition of the complementary event and its probability, the probability that the student owns neither a car nor a laptop is calculated as:

P [(A∪B)']= 1- P(A∪B)

P [(A∪B)']= 1 - 0.86

P [(A∪B)']= 0.14= 14%

Finally, the probability that the student owns neither a car nor a laptop is 14%.

Learn more about probability:

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