Question

Searches related to Jackson has received at least one text from Pedro on 45 of the last 50 days, and at least one text from Max on 40 of the last 50 days. Jackson has received at least one text from both Pedro and Max on 36 of the last 50 days. According to this data, are the events of getting at least one text from Pedro and at least one text from Max dependent or independent?

Answer 1

Since
`P(A \cap B) = P(A) * P(B)`, the events of getting at least one text from Pedro and at least one text from Max are independent.

Explanation:

Two events, A and B, area independent if:

`P(A \cap B) = P(A) * P(B)`

In this question:

Event A: getting at least one text from Pedro.

Event B: getting at least one text from Max.

Jackson has received at least one text from Pedro on 45 of the last 50 days:

This means that
`P(A) = (45)/(50) = 0.9`.

Jackson has received at least one text from Max on 40 of the last 50 days:

This means that
`P(B) = (40)/(50) = 0.8`

Jackson has received at least one text from both Pedro and Max on 36 of the last 50 days.

This means that
`P(A \cap B) = (36)/(50) = 0.72`

Verify dependency:

We have that
`P(A \cap B) = 0.72`.

`P(A) * P(B) = 0.9 * 0.8 = 0.72`

Since
`P(A \cap B) = P(A) * P(B)`, the events of getting at least one text from Pedro and at least one text from Max are independent.