If p (a|b) = 0.35, p (b) = 0.75 and p (a) = 0.44 are the events a and b independent?

Question

Rhett Ross

Mathematics

1 January, 05:12

If p (a|b) = 0.35, p (b) = 0.75 and p (a) = 0.44 are the events a and b independent?

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Answers (1)

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Antony Butler · Answer 1

Hello:

note 1:

p (A|B) = p (A∩B) / p (B)

note 2:

A and B independent: p (A∩B) = p (A) * p (B)

calculate : p (A∩B)

p (A∩B) = p (A|B) * p (B)

p (A∩B) = 0.35 * 0.75 = 0.2625

but : p (A) * p (B) = 0.44*0.75 = 0.33

conclusion:

the events A and B are not independent?