The probability for event A is 0.4, the probability for event B is 0.2, and the probability of events A and B is 0.1. Why are the events are not independent?

Question

asked Nov 24, 2021 78.1k views

2 Answers

Timaschew · Answer 1 · 2021-11-28T23:52:49+0000

Answer:

Since
$P(A \cap B) \\eq P(A)P(B)$ , these events are not independent.

Explanation:

Independent events:

Two events, A and B are independent, if:

$P(A \cap B) = P(A)P(B)$

In this question, we have that:

$P(A) = 0.4, P(B) = 0.2, P(A \cap B) = 0.1$

However

P(A)P(B) = 0.4*0.02 = 0.08

Since
$P(A \cap B) \\eq P(A)P(B)$ , these events are not independent.