Question

If \(A\) and \(B\) are independent events, \(P(A)=0.3\) and \(P(B)=0.4\), then \(P(A\cap B)=\) ?

• A. \(0.12\)
• B. \(0.21\)
• C. \(0.75\)
• D. \(0.7\)

Hint:

Independent $\Rightarrow$ multiply: \(P(A\cap B)=P(A)P(B)\). (If they were not independent, this formula would not hold.)

Answer 1

The Correct Option is A

Why we can multiply: For independent events, knowing that one happens does not change the chance of the other. By definition, this gives the multiplication rule \[ P(A\cap B)=P(A)\cdot P(B). \] Substitute the given probabilities: \[ P(A\cap B)=0.3\times 0.4=0.12. \] So the probability that both \(A\) and \(B\) occur together is \(0.12\).