math
posted by sha .
if E and F are independent events, find P(F) if P(E)=0.2 and P(E U F)= 0.3

math 
Reiny
If F and E are independent events then P(E and F) = 0
and we also know
P(E or F) = P(E) + P(F)  P(E and F)
.3 = .2 + P(F)  0
P(F) = .1 
math 
David
Let P(F)= X
since E and F are independent eveents,
P(EnF)= P(E)* P(F)
therefore, P(EnF)= 0.2X
but P(EuF)=P(E)+ P(F) P(EnF)
0.3= 0.2 + x  0.2x
x = 1/8 
math 
David
sorry, i made a mistake, for mutually exculsive events, P(EnF)= 0, hence,
from the previous equation,
0.3=0.2+P(F)0
so P(F)= 0.1 
Medical Physics 
Andre
Independent does not mean mutually exclusive, thus
P(EUF)=P(E)+P(F)P(EnF)
Independence allows us to write:
P(EUF)=P(E)+P(F)P(E)P(F)
P(EUF)=P(E)+[1P(E)]P(F)
Therefore,
P(F)= [P(EUF)P(E)]/[1P(E)]
P(F)=[0.30.2]/[10.2]
=.1/.8
=1/8
Respond to this Question
Similar Questions

Probability
three fair dice are tossed. Let X,Y,Z denote the respetive numbers showing on their top faces. Assume X,Y,Z are independent. a) find P(X<Y) b) Show that the events (X<Y) and (Y<Z) are NOT independent heeelp... 
Probability
Show that if events A B and C are independent that the following pairs of events are also independent: a) A and B Union C b) A  B and C 
Math
In exercises 1 and 2, use the following information. You randomly draw letter tiles from a bag containing the letters from the word PROBABILITIES. 1. You randomly select a B. You replace it. Then you choose a T. Tell whether the events … 
math
You randomly draw letter tiles from a bag containing the letters from the word INDEPENDENT. 1. You randomly draw an N. Then, without replacing the first letter, you pick a D. Tell whether the events are independent or dependent. Then … 
Math
If independent events have probabilities p and q, what are the odds of at least one of the events occurring? 
math
If A and B are independent events, P(A) = 0.35, and P(B) = 0.55, find the probabilities a) P(A intersected B) b) P(A united B) 
stats
you are given the probabilities listed below P(A)= 0.25, P(B) = 0.30, P(C)=0.55, P(A&C) = 0.05, P(B&C)=0, P(B/A)=0.48. A) ARE A AND B INDEPENDENT? 
probability & statistics
Q: if A and B are independent events, how many of the following statements must be true? 
statistics
Define the concept of independent events with regards to probability. Provide an example of an event that is independent and an event that is not independent 
statistics
For two events, C and D, P(C)=.16 and P(D)=.18 If C and D are independent events, then find P(D intersect C) and P(C given D) and P(D U C)