If $P (A) = 0.7, P (B) = 0.9$ $P(A) = 0.7, P(B) = 0.9$ and $P (A \cap B) = .4$ $P(A nn B)=.4$ . What is $P (B ∣ A)$ $P(B|A)$ ? What about $P (A ∣ B)$ $P(A|B)$ ?

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If $P (A) = 0.7, P (B) = 0.9$ $P(A) = 0.7, P(B) = 0.9$ and $P (A \cap B) = .4$ $P(A nn B)=.4$ . What is $P (B ∣ A)$ $P(B|A)$ ? What about $P (A ∣ B)$ $P(A|B)$ ?

1 Answer

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Answer 1 · 2015-10-27T19:36:14

$P (B ∣ A) = \frac{4}{7}$ $P(B|A)= 4/7$ and $P (A ∣ B) = \frac{4}{9}$ $P(A|B)= 4/9$

Explanation:

$P (B ∣ A) = \frac{P (A \cap B)}{P (A)} = \frac{0.4}{0.7} = \frac{4}{7}$ $P(B|A)=(P(A nn B))/(P(A))=(0.4)/(0.7)=4/7$
$P (A ∣ B) = \frac{P (A \cap B)}{P (B)} = \frac{0.4}{0.9} = \frac{4}{9}$ $P(A|B)=(P(A nn B))/(P(B))=(0.4)/(0.9)=4/9$

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If $P (A) = 0.7, P (B) = 0.9$ $P(A) = 0.7, P(B) = 0.9$ and $P (A \cap B) = .4$ $P(A nn B)=.4$ . What is $P (B ∣ A)$ $P(B|A)$ ? What about $P (A ∣ B)$ $P(A|B)$ ?

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Explanation:

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If P(A)=0.7,P(B)=0.9P(A) = 0.7, P(B) = 0.9 and P(A∩B)=.4P(A nn B)=.4. What is P(B∣A)P(B|A)? What about P(A∣B)P(A|B)?

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If $P (A) = 0.7, P (B) = 0.9$ $P(A) = 0.7, P(B) = 0.9$ and $P (A \cap B) = .4$ $P(A nn B)=.4$ . What is $P (B ∣ A)$ $P(B|A)$ ? What about $P (A ∣ B)$ $P(A|B)$ ?