SOLUTION: 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!

Question 1194098: 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!
Found 3 solutions by Boreal, ikleyn, greenestamps:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
Draw this out.
P(U)=0.64
P(V)=0.36
P(both) is 0.18
prob. of one or the other is 0.64+0.36-0.18=0.82.
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If it is V (probability of 0.36), the probability it is U is 0.18, half of 0.36, so the answer to the conditional probability is 0.50.

Answer by ikleyn(52784)   (Show Source): You can put this solution on YOUR website!
.
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!
~~~~~~~~~~~~~~~~

P(U|V) is so called "conditional probability" : it is the probability of event U given V. By the definition, P(U|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) = = = 0.5 = 50%. ANSWER

Solved, completed and completely explained.

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Notice that in this problem, the value P(U) = 0.64 is EXCESSIVE and UNNECESSARY : it is NOT USED 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, there are several lessons about conditional probability. They are
    - Conditional probability problems
    - Conditional probability problems REVISITED
    - More problems on Conditional probability

Read them to develop your skills and knowledge.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

The response from tutor @ikleyn shows the conditional probability formula and a full solution to the problem.

The response also states that the concept of conditional probability is difficult for beginners.

That was true for me; and I see it often among students first working with the concept.

So let me take a moment to try to explain why the formula is what it is.

The basic probability equation is
good outcomes P(desired outcome) = ------------------------ all possible outcomes

The conditional probability P(U|V) is the probability that U happens, GIVEN THAT V happens. That means the only outcomes we are considering are those in which V happens -- so the denominator of the probability fraction ("all possible outcomes") is P(V).

Then the numerator of the probability fraction ("good outcomes") is the probability that U ALSO happens (i.e., U and V BOTH have to happen) -- so the numerator is P(U AND V).

And so the conditional probability formula is
P(U AND V) P(U|V) = --------------- P(V)

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