Question 1172995
.
Suppose the probability of snow is 20%, and the probability of a traffic accident is 10%. Suppose further that 
the conditional probability of an accident, given that it snows, is 40%. What is the conditional probability 
that it snows, given that there is an accident?
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            It is a good question.

            Prepare yourself to read my solution very attentively.



<pre>
This problem relates, as you may conclude from the text, to <U>conditional probability</U>.


Let A be the event of snow.              Its probability is  20% = 0.2  (given).    (1)

Let B be the event of traffic accident.  Its probability is  10% = 0.1  (given).    (2)


The event of an accident, given that it snows, is the conditional probability  P(B|A).


This conditional probability  P(B|A)  is the ratio  P(B|A) = P(A &#8745; B) / P(A).


Its value is given by the condition : it is  P(B|A) = 40% = 0.4.  So,  P(A &#8745; B) / P(A) = 0.4.    (3)



Having  known (3) and (1), you can calculate  P(A &#8745; B) = 0.4 * P(A) = 0.4 * 0.2 = 0.08.



        It is the key step in the solution:  from the given data we managed to determine that  P(A &#8745; B) = 0.08.

        At this point, make a deep breath, and we will go further.



The problem asks us about OTHER conditional probability  P(B|A)  of the event  "snows, given that there is an accident".


This conditional probability is the ratio  P(B|A) = P(A &#8745; B) / P(B).


We just know  P(A &#8745; B), which is 0.08 (see (4) ). And we know P(B) = 0.1 (given)  (see (2) ).


THEREFORE,  P(B|A) = P(A &#8745; B) / P(B) = {{{0.08/0.1}}} = 0.8.


The problem is just solved and you get the


<U>ANSWER</U>.  The conditional probability that it snows, given that there is an accident, is 0.8.
</pre>

Solved.


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The better solution and better explanation you will find NOWHERE.


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On conditional probability, &nbsp;see my lessons

&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> 

in this site.


Read them to develop your skills and knowledge.



Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic &nbsp;"<U>Solved problems on Probability</U>" 
and &nbsp;"<U>Additional problems on Probability</U>". 



Save the link to this textbook together with its description


Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson


into your archive and use when it is needed.