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26/12/2021 2:15 pm
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P(A) = p, P(B) = 2p P(exactly one of them occur) = 5/9 then Pmax = ?
1 Answer
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26/12/2021 2:27 pm
P(A) = p, P(B) = 2p
P(A ∪ B) - P(A ∩ B) = \(\frac{5}{9}\)
3p - 2p (A ∩ B) = \(\frac{5}{9}\)
∴ P(A ∩ B) = \(\frac{3}{2}\)p - \(\frac{5}{18}\)
Also, P(A ∪ B) ≤ 1
\(\frac{3p}{2}\) + \(\frac{5}{18}\)≤ 1
\(\frac{3p}{2}\) ≤ \(\frac{13}{18}\)
∴ p ≤ \(\frac{13}{27}\)
Pmax = \(\frac{13}{27}\)