A probability problem by Nazmus sakib

Probability Level 1

If P ( A ∩ B ) = 1 6 , P ( A ∪ B ) = 5 6 , P ( A ) = 1 6 P(A \cap B) = \dfrac{1}{6}, P(A \cup B) = \dfrac{5}{6}, P(A) = \dfrac{1}{6}

then what is the value of P ( B ) ? P(B)?

5 6 \dfrac{5}{6} 2 3 2 \dfrac{3}{2} 6

Nazmus Sakib by Nazmus sakib , 24, Bangladesh

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1 solution

Hana Wehbi
Oct 11, 2017

If P ( A ∩ B ) = 1 6 , P ( A ∪ B ) = 5 6 , P ( A ) = 1 6 P(A \cap B) = \dfrac{1}{6}, P(A \cup B) = \dfrac{5}{6}, P(A) = \dfrac{1}{6}

then the value of P ( B ) = P ( A ∪ B ) + P ( A ∩ B ) − P ( A ) = 5 6 + 1 6 − 1 6 = 5 6 P(B) = P(A\cup B) + P(A\cap B) -P(A) = \frac{5}{6} +\frac{1}{6} - \frac {1}{6} = \frac{5}{6}

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