To find the probability of the union of two independent events A and B, we can use the following formula:
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
Since A and B are independent events, the probability of their intersection can be calculated as:
P(A ∩ B) = P(A) × P(B)
Now, substituting the given probabilities:
- P(A) = 0.4
- P(B) = 0.1
First, we calculate P(A ∩ B):
P(A ∩ B) = P(A) × P(B) = 0.4 × 0.1 = 0.04
Now, we can substitute this value back into the union formula:
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
P(A ∪ B) = 0.4 + 0.1 – 0.04
P(A ∪ B) = 0.5 – 0.04 = 0.46
Therefore, the probability of A union B, P(A ∪ B), is 0.46.