SOLUTION: A driver has 3 routes to get his produce from factory to ;the port. He uses route 1; 45% of the time, route 2 ; 35% of the time and route 3; 20% of the time. There is a 70% probabi

Algebra ->  Finance -> SOLUTION: A driver has 3 routes to get his produce from factory to ;the port. He uses route 1; 45% of the time, route 2 ; 35% of the time and route 3; 20% of the time. There is a 70% probabi      Log On


   

Question 1192749: A driver has 3 routes to get his produce from factory to ;the port. He uses route 1; 45% of the time, route 2 ; 35% of the time and route 3; 20% of the time. There is a 70% probability of encountering traffic jam on route 1, 40% probability of encountering traffic jam on route 2 and 50% probability of encountering traffic jam on route 3.
ii)If a driver reports that he is in a traffic jam, find the probability that he has selected route 3. I would do :Jam on route 3/ total probability of all Jams
.5/(.45*.7 + .35*.4 + .2*.5)
Please I am seeking some help in finding the correct solution.
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
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A driver has 3 routes to get his produce from factory to ;the port.
He uses route 1; 45% of the time, route 2 ; 35% of the time and route 3; 20% of the time.
There is a 70% probability of encountering traffic jam on route 1, 40% probability
of encountering traffic jam on route 2 and 50% probability of encountering traffic jam on route 3.
ii)If a driver reports that he is in a traffic jam, find the probability that he has selected route 3.
I would do :Jam on route 3/ total probability of all Jams
.5/(.45*.7 + .35*.4 + .2*.5)
Please I am seeking some help in finding the correct solution.
~~~~~~~~~~~~~~~~~~ 

The correct formula is


    P = %280.2%2A0.5%29%2F%280.45%2A0.7+%2B+0.35%2A0.4+%2B+0.2%2A0.5%29.    (1)



This problem is about conditional probability.


Conditional probability of event A given event B is  P(A|B) = P%28A_and_B%29%2FP%28B%29.    (2)


Notice that the numerator of the formula is the probability of INTERSECTION of events A and B.


So, when you apply this basic formula (2) (the definition of the conditional probability),
you will get formula (1).

Solved and explained.

Happy learning (!)

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On conditional probability,  see the lessons
    - Conditional probability problems
    - Conditional probability problems REVISITED
    - More problems on Conditional probability
in this site.

Read them to develop your skills and knowledge.

Also,  you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic  "Solved problems on Probability"
and  "Additional problems on Probability".


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.