Question

the 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? because no yes

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 \(0.25
eq0.15\), the events are not independent.

Answer:

No, because \(P(A)\times P(B)
eq P(A\cap B)\)