Let P(A) 0.4 & P(B|A) = 0.5. The propability is equal to __________

Engineering

Mathematics

Conditional Probability

Question

Let P(A) 0.4 & P(B|A) = 0.5. The propability $P (\bar{A} \cup \bar{B})$ is equal to ___________.

0.8

0.7

0.6

None of these

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Given P(A) = 0.4, P(B|A) = 0.5

$P (\bar{A}) = 1 - P (A)$

= 1 – 0.4

= 0.6

$P (\frac{B}{A}) = \frac{P (A \cap B)}{P (A)}$

$0.5 = \frac{P (A \cap B)}{(0.4}$

⇒ P(A⋂B) = 0.2

So, $P (\bar{A} \cup \bar{B}) = P (A \cap B)^{'}$

= 1 – P(A⋂B)

= 1 – 0.2

= 0.8

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