If P A -2-5- P B -1-3- P A - B -1-5- then find P A - B -

As P(A̅|B̅ )=P(A̅∩B̅ )/P(B̅ ) ⇒ =1 P(A∪ B)/1 P(B) ⇒ =1 [P(A)+P(B) P(A∩ B) ]/1 1/3 ⇒ =1 [2/5+1/3 1/5 ]/2/3=7/10. ...

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Union of Sets

If P A =2/5, ...

Question

If $P (A) = \frac{2}{5}, P (B) = \frac{1}{3}, P (A \cap B) = \frac{1}{5}$ , then find $P (¯ A | ¯ B) .$

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Solution

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P (A) = 2 / 5, P (B) = 1 / 3, P (A \cap B) = 1 / 5

P (A / B)

P (A) = \frac{2}{5}

P (B) = \frac{3}{10}

P (A \cap B) = \frac{1}{5}

P (A^{'} | B^{'}) . P (B^{'} | A^{'})

P (B) = \frac{3}{5}, P (A | B) = \frac{1}{2}

P (A \cup B) = \frac{4}{5}

P (A \cup B)^{'} + P (A^{'} \cap B)

P (A) = \frac{1}{4}, P (¯ ¯¯ ¯ B) = \frac{1}{2}

P (A \cup B) = \frac{5}{9}

P (A / B)

P (A) = \frac{1}{4}

P (B) = \frac{1}{2}

P (A \cup B) = \frac{5}{8}

P (A \cap B)

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