Question 1194098
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U and V are two events. P(U) = 0.64; P(V) = 0.36, and P(U AND V) = 0.18. Find P(U|V)
Please show work so I can understand how to answer the question. Thank you!
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<pre>
P(U|V) is so called  "conditional probability" :  it is the probability of event U given V.


By the definition, P(U|V) = {{{P(U_AND_V)/P(V)}}} :   it is the probability of P(U AND V),  divided by P(V).



All parts of this ratio are given to you: 

    the numerator is P(U AND V) = 0.18;  the denominator P(V) = 0.36.



So, you simply substitute these given values into the formula, and you immediately get

    P(U|V) = {{{0.18/0.36}}} = {{{1/2}}} = 0.5 = 50%.    <U>ANSWER</U>
</pre>

Solved, completed and completely explained.


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Notice that in this problem, the value &nbsp;P(U) = 0.64  &nbsp;is &nbsp;EXCESSIVE &nbsp;and &nbsp;UNNECESSARY : &nbsp;it is &nbsp;NOT &nbsp;USED &nbsp;in the solution.



The conception of conditional probability is one which is difficult to understand for beginners.


Only steady move step by step from simple problems to more complicated may help,

along with solution of many problems.


In this site, &nbsp;there are several lessons about conditional probability. They are

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Conditional-probability-problems.lesson>Conditional probability problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/More-conditional-probability-problems.lesson>Conditional probability problems REVISITED</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/More-problems-on-Conditional-probability.lesson>More problems on Conditional probability</A> 


Read them to develop your skills and knowledge.