Engineering
Mathematics
Addition Theorem on Probability
Basic Definitions Related to Probability
Question
If P(AUB) = P(A⋂B) ⇔ then show that relation between P(A) and P(B) is P(A) = P(B).
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Solution
P(AUB) = P(A) + P(B) – P(A⋂B)
If P(AUB) = P(A⋂B)
Then P(A) and P(B) are equal
Since P(AUB) = P(A⋂B) ⇒ A and B are equal sets
Thus P(A) and P(B) are equal to P(A⋂B)