Question

In: Statistics and Probability

Use a process of throwing one unbiased dice (equal outcomes from 1 to 6) to give...

  1. Use a process of throwing one unbiased dice (equal outcomes from 1 to 6) to give examples and explain why:
    1. Elementary event [1]

  1. Composite event [1]

  1. Two mutually exclusive composite events [2]

  1. Two dependent events [3]

  1. Two independent events [3]

  1. A composite event and its complimentary event [2]
  1. Use a process of throwing one unbiased dice (equal outcomes from 1 to 6) to give examples and explain why:
    1. Elementary event [1]

  1. Composite event [1]

  1. Two mutually exclusive composite events [2]

  1. Two dependent events [3]

  1. Two independent events [3]

  1. A composite event and its complimentary event [2]

Solutions

Expert Solution

Elementary event-

The elementary events are

  • Obtaining 1
  • Obtaining 2
  • Obtaining 3
  • Obtaining 4
  • Obtaining 5
  • Obtaining 6

Composite event-

Composite events consists of more than one elementary events.

Some examples of composite events are

  • Obtaining even
  • Obtaining prime
  • Obtaining values greater than 4

Two mutually exclusive composite events-

Two events are mutually exclusive if these are disjoint.

An example of two mutually exclusive composite events is as follows.

,

Clearly, and

So, events A and B are mutually exclusive.

Two dependent events-

Two events are dependent if occurrence of one is influenced by other. In case of dependence of two events A and B,

An example of two dependent events is as follows.

,

Clearly, and

Two independent events-

Two events are independent if occurrence of one is not influenced by other. In case of independence of two events A and B,

An example of two dependent events is as follows.

,

Clearly, and

A composite event and its complimentary event-

An example of composite event is

Hence, a composite event is obtaining odd numbers and its complement event is obtaining even numbers.

orchestra answered 2 years ago
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