Question

ebra i b-cr
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 not independent?
○ the sum of p(a) and p(b) is greater than p(a and b).
○ the product of p(a) and p(b) is greater than p(a and b).
○ the product of p(a) and p(b) is not equal to p(a and b).
○ the sum of p(a) and p(b) is not equal to p(a and b).

Explanation:

Step1: Recall independence rule

Two events A and B are independent if $P(A \text{ and } B) = P(A) \times P(B)$.

Step2: Calculate $P(A) \times P(B)$

$P(A) \times P(B) = 0.4 \times 0.2 = 0.08$

Step3: Compare to $P(A \text{ and } B)$

Given $P(A \text{ and } B) = 0.1$, and $0.08
eq 0.1$.

Answer:

The product of P(A) and P(B) is not equal to P(A and B).