Probability Theory

$P(A') = 1 - P(A)$. The event either happens or it does not.

The union is inclusive — it covers the case where both events happen.

For independent events $P(A\cap B) = P(A)P(B) = 0.6 \times 0.5 = 0.3$.

$0.4 + 0.3 - 0.1 = 0.6$. The subtraction removes the double-counted overlap.

$P(A\mid B) = 0 \ne P(A)$, so independence fails. Mutually exclusive and independent are opposite ideas, not similar ones.

Use the complement: $P(\text{no green}) = \dfrac58 \times \dfrac47 = \dfrac{20}{56} = \dfrac{5}{14}$, so the answer is $1 - \dfrac{5}{14} = \dfrac{9}{14}$.