Identify Given Data

We are given the probabilities of two independent events $A$ and $B$: $P(A) = 0.3$ and $P(B) = 0.5$.

$P(A) = 0.3, \quad P(B) = 0.5$

Use Independence Property

Since events $A$ and $B$ are independent, the probability of both events occurring together is the product of their individual probabilities: $P(A \cap B) = P(A) \times P(B)$.

$P(A \cap B) = 0.3 \times 0.5 = 0.15$

Apply Addition Theorem

The probability of either event $A$ or event $B$ occurring is given by the addition theorem for probability.

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

Calculate Final Value

Substitute the known values into the equation to compute the final result.

$P(A \cup B) = 0.3 + 0.5 - 0.15 = 0.65$