Chapter 10.2, Problem 1E

To determine

To explain:

The comparison between independent and dependent events with example

Answer to Problem 1E

The probability of independent and dependent events is not affected and affected by another events happening respectively.

Explanation of Solution

In real life and in statistics the events are classified as independent and dependent events. Let’s check them in detail:

Dependent events:

If another event occurs first which gives an influence for the next events then the events is known as dependent events.

Here, the probability of the common events is not the product of the individual of each event occurs as:

  $P\left(A\cap B\right)\ne P\left(A\right)P\left(B\right)$

Where,

Two events: $A,B$

Example:

If you park your vehicle illegally, you’re more expected to acquire a parking permit.

Independent events:

An event is called as independent event when it is not connected to another event or its probability is not happening, happening or conversely.

Or in the simple words the independent events are those events which contain the probability of the common events. The probability of the common events is nothing but the product of the individual of each event occurs in the series as

  $P\left(A\cap B\right)=P\left(A\right)\times P\left(B\right)$

Where,

Two independent events: $A,B$

Example:

Taking an Uber ride and getting a free meal at your favorite restaurant