SOLUTION: The probability that an event A occurs is P(A) = 0.4. B is an event
independent of A and P(A U B) = 0.7. Find P (B).

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Question 1203256: The probability that an event A occurs is P(A) = 0.4. B is an event
independent of A and P(A U B) = 0.7. Find P (B).
Answer by ikleyn(52790)   (Show Source): You can put this solution on YOUR website!
.
The probability that an event A occurs is P(A) = 0.4.
B is an event
independent of A and P(A U B) = 0.7. Find P (B).
~~~~~~~~~~~~~~~~~~ 

Start from general formulas

    P(A U B) = P(A) + P(B) - P(A n B),  P(A n B) = P(A)*(P(B).


Substitute the given data there.  You will get

   0.7 = 0.4 + P(B) - 0.4*P(B).


Simplify

    0.7 - 0.4 = P(B) - 0.4*P(B),

    0.3 = 0.6*P(B)

    P(B) =  = 0.5.


ANSWER.  P(B) = 0.5.

Solved.



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