Probability

X and Y represent two events such that P(X)=1/4; P(X U Y)=3/4a) If X and Y are independent but not mutually exclusive then P(Y)=?

So far i have that P(X U Y)=P(X) + P(Y) - P(X).P(Y)
3/4=1/4 + P(Y) - 1/4 * P(Y)
AND THEN I GET STUCK PLEASE HELP


b)If X and Y are independent then P(X ∩ Y)= ?

AS I DONT know part A i can't do this
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417459n said:

X and Y represent two events such that P(X)=1/4; P(X U Y)=3/4a) If X and Y are independent but not mutually exclusive then P(Y)=?

So far i have that P(X U Y)=P(X) + P(Y) - P(X).P(Y)
3/4=1/4 + P(Y) - 1/4 * P(Y)
AND THEN I GET STUCK PLEASE HELP


b)If X and Y are independent then P(X ∩ Y)= ?

AS I DONT know part A i can't do this

Click to expand...

Keep going with part (a):

\(\displaystyle \frac{3}{4}=\frac{1}{4}+P(Y)-\frac{1}{4}P(Y)\)

\(\displaystyle \frac{3}{4}-\frac{1}{4}=\frac{4}{4}P(Y)-\frac{1}{4}P(Y)\)

\(\displaystyle \frac{2}{4}=\frac{3}{4}P(Y)\)

\(\displaystyle \frac{1}{2}\cdot\frac{4}{3}=P(Y)\)

\(\displaystyle \frac{2}{3}=P(Y)\)

417459n said:

X and Y represent two events such that P(X)=1/4; P(X U Y)=3/4a) If X and Y are independent but not mutually exclusive then P(Y)=?

So far i have that P(X U Y)=P(X) + P(Y) - P(X).P(Y)
3/4=1/4 + P(Y) - 1/4 * P(Y)
AND THEN I GET STUCK PLEASE HELP


b)If X and Y are independent then P(X ∩ Y)= ?

AS I DONT know part A i can't do this

Click to expand...

Part (b) has nothing to do with part (a)! What is the definition of "independent"?