SOLUTION: The probability of an outcome X is 1/5, the probability of another outcome is 1/4. If the probability of an outcome X or Y or both is 2/5 find the probability of X and Y

Algebra ->  Probability-and-statistics -> SOLUTION: The probability of an outcome X is 1/5, the probability of another outcome is 1/4. If the probability of an outcome X or Y or both is 2/5 find the probability of X and Y      Log On


   

Question 1152280: The probability of an outcome X is 1/5, the probability of another outcome is 1/4. If the probability of an outcome X or Y or both is 2/5 find the probability of X and Y
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
.
The probability of an outcome X is 1/5, the probability of another outcome is 1/4.
If the probability of an outcome X or Y highlight%28cross%28or_both%29%29 is 2/5 find the probability of X and Y
~~~~~~~~~~~~~~~~~~ 



Use the general formula of the Probability theory


P(X or Y) = P(X) + P(Y) - P(X and Y).


You are given ALL input data.


Substitute and calculate.  Do it on your own.

Happy calculations (!)




Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
p(x) = 1/5
p(y) = 1/4
p(x or y) = 2/5
find p(x and y)
formula to use is:
p(x or y) = p(x) + p(y) - p(x and y)
this becomes:
2/5 = 1/5 + 1/4 - p(x and y)
add p(x and y) from both sides of the equation and subtract 2/5 from both sides of the equation to get:
p(x and y) = 1/5 + 1/4 - 2/5
place all fractions under common denominator of 20 to get:
p(x and y) = 4/20 + 5/20 - 8/20
solve for p(x and y) to get:
p(x and y) = 1/20
that's your solution.