Question

A and B are two events.

Given that P(A)=0.25 , P(B)=0.3 and P(AandB)=0.05 .

Drag and drop the answers into the boxes.

Answer 1

Events A and B are not independent because
`P(A / B) \\eq P(A)`

Explanation:

Given that
`P(A)=0.25`,
`P(B)=0.3` and
`P(A \text { and } B)=0.05`

Two events are said to be independent events, if it satisfies any one of the following conditions,

`P(A / B) = P(A)` or
`P(B / A) = P(B)` or
`P(AB)=P(A)P(B)`

First, let us substitute the values in the equation
`P(A / B) = P(A)`

The formula to find
`P(A / B)` is
`P(A / B)=(P(A \cap B))/(P(B))`

Substituting the values, we get,

`P(A / B)=(0.05)/(0.3) =0.1667`

But
`P(A)=0.25`

Hence,
`P(A / B) \\eq P(A)`

Thus, A and B are not independent events.