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If p(a) =. 35 and p(b) =. 45 and p(a and b) =. 25, then p(b|a) is

Sagot :

ghanami

Answer:

p(b|a) =5/7

Step-by-step explanation:

hello :

note : p(b|a) = p(a and b)/p(a)

p(b|a) = 25/35 =5/7

The value of the probability of the event B given A, symbolically P(B|A), when it is known that P(A) = 0.35, P(B) = 0.45 and P(A∩ B) =0.25 is found as: P(B|A) = 5/7

What is chain rule in probability?

For two events A and B, by chain rule, we have:

[tex]P(A \cap B) = P(B)P(A|B) = P(A)P(B|A)[/tex]

where P(A|B) is probability of occurrence of A given that B already occurred.

We're given that:

  • P(A) = 0.35
  • P(B) = 0.45
  • P(A and B) = P(A ∩ B) = 0.25
  • P(B|A) = to be known.

Using the chain rule of probability, we get:

[tex]P(A \cap B) = P(A)P(B|A) \\\\P(B|A) = \dfrac{P(A \cap B)}{P(A)} = \dfrac{0.25}{0.35} = \dfrac{5}{7}[/tex]

Thus, the value of the probability of the event B given A, symbolically P(B|A), when it is known that P(A) = 0.35, P(B) = 0.45 and P(A∩ B) =0.25 is found as: P(B|A) = 5/7

Learn more about chain rule here:

https://brainly.com/question/21081988

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