Maths · Probability: Probability of an event, addition and multiplication theorems of probability
If =\boldsymbol{P}(\boldsymbol{B}), \) then the two events and are -
If \( \boldsymbol{P}(\boldsymbol{A})=\boldsymbol{P}(\boldsymbol{B}), \) then the two events \( \boldsymbol{A} \) and \( B \) are -
- A. Independent
- B. Dependent
- C. Equally likely
- D. Both (A) and (C)
Step-by-step solution
Given P(A)=P(B), the events have the same probability of occurrence, so they are equally likely. Independence requires P(A∩B)=P(A)P(B), which is not assured, and dependence is also not implied. Thus, only option C is correct.
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