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Union of Sets

If PB=34, P...

Question

If $P (B) = \frac{3}{4}, P (A \cap B \cap ¯ C) = \frac{1}{3},$ then find the value of $P (B \cap C)$

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Solution

We have $P (B \cap C) = P (B) - P (A \cap B \cap ¯ C) - P (¯ A \cap B \cap ¯ C)$
$= \frac{3}{4} - \frac{1}{3} - \frac{1}{3}$
$= \frac{3}{4} - \frac{2}{3} = \frac{9 - 8}{12} = \frac{1}{12}$

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P (B) = \frac{3}{4}, P (A \cap B \cap ¯ C) = \frac{1}{3}

P (¯ A \cap B \cap ¯ C) = \frac{1}{3}

P (B \cap C)

P (B) = \frac{3}{4}, P (A \cap B \cap ¯ C) = \frac{1}{3} a n d P (¯ A \cap B \cap ¯ C) = \frac{1}{3}

P (B \cap C) = \frac{λ}{μ}

λ

μ

are coprime, then

μ - 5 λ

P (B) = \frac{3}{4}, P (A \cap B \cap ¯ ¯¯ ¯ C) = \frac{1}{3}

P (¯ ¯¯ ¯ A \cap B \cap ¯ ¯¯ ¯ C) = \frac{1}{3}

P (B \cap C)

P (\frac{A}{C}) > P (\frac{B}{C})

P (\frac{A}{¯ C}) > P (\frac{B}{¯ C})

then the relationship between

P (A)

P (B)

P (B) = \frac{3}{4}, P (A \cap B \cap ¯ ¯¯ ¯ C) = \frac{1}{3}

P (¯ ¯¯ ¯ A \cap B \cap ¯ ¯¯ ¯ C) = \frac{1}{3}

P (B \cap C)

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