using the multiplication rule to determine if events are independent\nthe probability for event a is 0.3…

using the multiplication rule to determine if events are independent\nthe probability for event a is 0.3, the probability for event b is 0.5, and the probability of events a and b is 0.25. are the events independent?\n, because

using the multiplication rule to determine if events are independent\nthe probability for event a is 0.3, the probability for event b is 0.5, and the probability of events a and b is 0.25. are the events independent?\n, because

Answer

Explanation:

Step1: Recall independence formula

For two independent events (A) and (B), (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 are given (P(A\cap B)=0.25). Since (0.15\neq0.25), the events are not independent.

Answer:

No, because (P(A)\times P(B)=0.3\times0.5 = 0.15\neq0.25 = P(A\cap B))