Probability (AND) question

jonnyenglish

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Mar 13, 2019
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Given that P(X) = 0.5, P(Y) = 0.45, and P(X|Y) = 0.3 which one of the following is the value of P(X and Y)?

A: 0.135 E: 0.15

B: 1.25 F: 0.8

C: 0.225 G: 0.85

D: 0.65 H: 0.95

Ok, assuming that it's an inderpendant event I think the answer is C

p(X) * p(Y) = P(X and Y)

0.5*0.45=0.225


but the booklet says the answer is A - what am I missing?
 

Dr.Peterson

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You can't assume two events are independent -- that is a very special situation. In fact, if they were, then P(X | Y) would equal P(X), which proves that they are not.

What is the definition of P(X | Y)? One form of definition is an equation that involves P(X), P(Y), and P(X and Y); you can then solve for what is asked.
 

jonnyenglish

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Hi, thanks for replying


What is the definition of P(X | Y)?

Sorry earlier in the booklet it is stated that P(A | B) denotes the probability of A occurring given that B has occurred
I’m aware that 0.3 * 0.45 = 0.135 but I still don’t understand why that is the correct answer.
 

Jomo

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P(A | B) = P(A and B) / P(B)
 

pka

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Given that P(X) = 0.5, P(Y) = 0.45, and P(X|Y) = 0.3 which one of the following is the value of P(X and Y)?
A: 0.135 E: 0.15
B: 1.25 F: 0.8
C: 0.225 G: 0.85
D: 0.65 H: 0.95
\(\displaystyle \mathscr{P}(X|Y)=\dfrac{\mathscr{P}(X\cap Y)}{\mathscr{P}(Y)}\)
\(\displaystyle 0.3=\dfrac{\mathscr{P}(X\cap Y)}{0.45}\)
\(\displaystyle \mathscr{P}(X\cap Y)=\;?\)
 
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