Question

There are events X, Y and Z. P(X) = 0.25, P(Y) = 0.04, and P(Z) = 0.3
P(X and Z) = 0.20, P(X and Z) = 0.075, and the P(Y and Z) = 0.015. Which of these two events are independent?

Answer 1

To determine if two events are independent, we need to compare the probability of their intersection to the product of their individual probabilities.

Let's compare events X and Z:
P(X and Z) = 0.20, P(X) = 0.25, P(Z) = 0.3
P(X and Z) = P(X) * P(Z)
0.20 = 0.25 * 0.3

Since the equation is true, events X and Z are independent.

Now let's compare events X and Y:
P(X and Y) = 0.075, P(X) = 0.25, P(Y) = 0.04
P(X and Y) = P(X) * P(Y)
0.075 ≠ 0.25 * 0.04

Since the equation is not true, events X and Y are not independent.

Therefore, event X and Z are independent, but event X and Y are not independent.