SOLUTION: Find probability of P(E and F) if P(E or F) = 0.60 If P((E) = 0.25 and P(F) = 0.40 I have never seen this particular structural format.

Algebra ->  Probability-and-statistics -> SOLUTION: Find probability of P(E and F) if P(E or F) = 0.60 If P((E) = 0.25 and P(F) = 0.40 I have never seen this particular structural format.       Log On


   

Question 1135919: Find probability of P(E and F) if P(E or F) = 0.60
If P((E) = 0.25
and P(F) = 0.40
I have never seen this particular structural format.
Answer by ikleyn(53763) About Me  (Show Source):
You can put this solution on YOUR website!
.

The formulation is THIS : 

    Find probability  P(E and F)  if  P(E or F) = 0.60,  P(E) = 0.25  and  P(F) = 0.40.


Solution 

There is nothing easier.


Use the general formula of the Probability Theory

    P(E or F) = P(E) + P(F) - P(E and F),

which is valid for any two events E and F.



From this formula, you will get

    P(E and F) = P(E) + P(F) - P(E or F),

which implies, after substituting the given data,

    P(E and F) = 0.25 + 0.40 - 0.60 = 0.65 - 0.60 = 0.05.


ANSWER.  P(E and F) = 0.05.

Solved.