SOLUTION: Let A and B be independent events with P(A) = 1/4 and P(B) = 1/5. Find P(A <font face = "symbol">Ç</font> B) and P(A<font face = "symbol">È</font>B).

Algebra ->  Probability-and-statistics -> SOLUTION: Let A and B be independent events with P(A) = 1/4 and P(B) = 1/5. Find P(A <font face = "symbol">Ç</font> B) and P(A<font face = "symbol">È</font>B).      Log On


   

Question 162537: Let A and B be independent events with P(A) = 1/4 and P(B) = 1/5. Find P(A Ç B) and P(AÈB).
Answer by Edwin McCravy(20056) About Me  (Show Source):
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Let A and B be independent events with P(A) = 1/4 and P(B) = 1/5. Find P(A Ç B) and P(AÈB). 


For independent events only (Two events are independent if it were true
that one on them were known to be certain, likely, unlikely, or impossible,
that knowledge would not affect the probability of the other at all.)

P(A Ç B) = P(A)*P(B) = 1%2F4*1%2F5 = 1%2F20

For any two events, whether independent or not,

P(A È B) = P(A) + P(B) - P(A Ç B)

P(A È B) = 1%2F4%2B1%2F5-1%2F20=5%2F20%2B4%2F20-1%2F20=8%2F20=4%2F5

Edwin