Given that \(P(\bar A)\) = 0.4, P(B) = 0.2 and \(P\left(\frac{A}{B}\ri

1.	Given that \(P(\bar A)\) = 0.4, P(B) = 0.2 and \(P\left(\frac{A}{B}\right) \) = 0.5. Find P(A ∪ B).
Answer» \(P(\bar A)=0.4\) ⇒ P(A) = 1 - 0.4 = 0.6 Now, \(P\left(\frac{A}{B}\right) = \frac{P(A\cap B)}{P(B)}\) ⇒ \(0.5=\frac{P(A\cap B)}{0.2}\) ⇒ P(A ∩ B) = 0.5 \(\times\) 0.2 = 0.1 Now P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.6 + 0.2 - 0.1 = 0.8 - 0.1 = 0.7

Given that \(P(\bar A)\) = 0.4, P(B) = 0.2 and \(P\left(\frac{A}{B}\right) \) = 0.5. Find P(A ∪ B).

Answer»

\(P(\bar A)=0.4\)

⇒ P(A) = 1 - 0.4 = 0.6

Now, \(P\left(\frac{A}{B}\right) = \frac{P(A\cap B)}{P(B)}\)

⇒ \(0.5=\frac{P(A\cap B)}{0.2}\)

⇒ P(A ∩ B) = 0.5 \(\times\) 0.2 = 0.1

Now P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

= 0.6 + 0.2 - 0.1 = 0.8 - 0.1

= 0.7

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Given that \(P(\bar A)\) = 0.4, P(B) = 0.2 and \(P\left(\frac{A}{B}\right) ​\) = 0.5. Find P(A ∪ B).

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Given that \(P(\bar A)\) = 0.4, P(B) = 0.2 and \(P\left(\frac{A}{B}\right) \) = 0.5. Find P(A ∪ B).