Posted by **sha** on Tuesday, July 27, 2010 at 12:12pm.

if E and F are independent events, find P(F) if P(E)=0.2 and P(E U F)= 0.3

- math -
**Reiny**, Tuesday, July 27, 2010 at 12:18pm
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**, Tuesday, July 27, 2010 at 2:49pm
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**, Tuesday, July 27, 2010 at 2:56pm
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**, Tuesday, December 8, 2015 at 3:23pm
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)+[1-P(E)]P(F)

Therefore,

P(F)= [P(EUF)-P(E)]/[1-P(E)]

P(F)=[0.3-0.2]/[1-0.2]

=.1/.8

=1/8

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