the probability for event a is 0.3, the probability for event b is 0.5, and the probability of events a and…

Explanation:

Step1: Recall independence formula

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

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

Given $P(A) = 0.3$ and $P(B)=0.5$, then $P(A)\times P(B)=0.3\times0.5 = 0.15$.

Step3: Compare with $P(A\cap B)$

We know $P(A\cap B)=0.25$. Since $0.25\neq0.15$, the events are not independent.

Answer:

No, because $P(A)\times P(B)=0.15$ and $P(A\cap B) = 0.25$ and $P(A\cap B)\neq P(A)\times P(B)$.