Maths · Probability: Probability of an event, addition and multiplication theorems of probability
If and are two events, such that or ) , \) then
If \( A \) and \( B \) are two events, such that \( P(A \) or \( \mathrm{B} \) ) \( =\mathrm{P}(\mathrm{A}), \) then
- A. events A and B are mutually exclusive
- B. events A and B are statistically independent
- C. event B is a subset of event A
- D. event A is a subset of event B
Step-by-step solution
Given P(A ∪ B) = P(A). Using P(A ∪ B) = P(A) + P(B) - P(A ∩ B), we get P(A) = P(A) + P(B) - P(A ∩ B) ⇒ P(B) = P(A ∩ B). This means the probability of B is entirely contained in A, implying B ⊆ A in the probabilistic sense.
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