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What is the probability of B if they are independent events P(A)= 3/7, P(A then B)=1/3?

Answer 1

Avery Alexander

#7/9#

#P(A->B)=P(A)*P(B)#

#1/3=3/7*P(B)#

#P(B)=(1/3)/(3/7)=7/9#

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Answer 2

Ethan Adkins

#P(B)=1/3.#

A Clarification : I interpret #P(A" then "B) as, P(B/A)#, i.e., the

Cond. Prob. of an event #B,# knowing that the event #A# has

already occurred.

So, if the events #A and B# are independent,

#P(B/A)=P(B)=1/3.#

In an otherway round, if we define, Independence of events

#A and B iff P(AnnB)=P(A)*P(B),# we get the same reult as follows:

#P(A" then "B)=P(B/A)=(P(BnnA))/(P(A))={P(B)*P(A)}/(P(A))=P(B).#

Enjoy Maths.!

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Answer 3

Hazel Anglin

The probability of event B occurring, given that events A and B are independent, is equal to the probability of event B occurring, which is ( P(B) ). Therefore, the probability of event B is ( P(B) = \frac{1}{3} ).

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