Let's Find The Other Single Event

Probability Level 1

Let A A and B B be two events such that P ( A ) = 0.3 P (A) =0.3 and P ( A ∪ B ) = 0.8 P (A \cup B) = 0.8 . If A A and B B are independent events, find P ( B ) P (B) .

5 7 \frac57 2 7 \frac27 7 23 \frac7{23} 6 35 \frac6{35}

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Umair Siddiqui by Umair Siddiqui , 23, India

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1 solution

0.8 = P ( A ∪ B ) = P ( A ) + P ( B ) − P ( A ∩ B ) = 0.8 = P(A \cup B) = P(A) +P(B) - P(A \cap B) = (A and B are independent events) = P ( A ) + P ( B ) − P ( A ) ⋅ P ( B ) = =P(A) + P(B) - P(A) \cdot P(B) = = P ( A ) + P ( B ) ⋅ ( 1 − P ( A ) ) = 0.3 + P ( B ) ⋅ ( 1 − 0.3 ) ⇒ = P(A) + P(B)\cdot(1 - P(A)) = 0.3 + P(B)\cdot (1 - 0.3) \Rightarrow P ( B ) = 0.5 0.7 = 5 7 P(B) = \frac{0.5}{0.7} = \frac{5}{7}

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nice solution

Umair Siddiqui - 5 years, 3 months ago

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