Question

describe real-life events that are:

1. Complementary
2. Mutually exclusive.
3. Not mutually exclusive.
4. Independent.
5. Dependent.

6. For each of the examples, you provide briefly explain how you know they are that type of event.

Answer 1

a) Complementary event:

Consider the workers in a factory.

Let A = { male workers}

Therefore A^c = { not male workers } = { female workers }

b) Mutually exclusive events:

Let A = Population of a particular city

B_x = { Number of peoples in a age group x to x + 1 } x =0, 1, 2, ....,n

Therefore B_x are mutually exclusive events for each value of x.

c) Not mutually exclusive events :

Consider, A = All the students who gives the exam in a class .

Let B = { Number of students passed in mathematics}

C = { Number of students who passed in statistics}

D = { Number of students who passed in both mathematics and statistics }.

Here assume that D include at least one sample element.

Therefore , D = A and B .

So that A and B are not mutually exclusive events.

d) Let X = Number of hours of study by the students in a particular class .

Y= Height of the students.

Then X and Y are independent events, because height is not affected to the number of hours study by the students.

e) Let X = Height of a person

Y = Weight of a person.

Here X and Y are dependent events.

Because, in general tallest peoples have more weight.