Question 1159315
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As it is worded and presented in the post, the problem is posed incorrectly.

The corrected formulation (corrected by me) is as follows:


<pre>
    A manufacture of air-conditioning units purchases 70% of its thermostats from company A, 20% from company B, 
    and the rest from company C. Past experience shows that 5% of company A’s thermostats, 1% of company B’s thermostats 
    and 1,5% of company C’s thermostats are likely to be found to have a defective thermostat.

    One thermostat was chosen randomly, and it was defective.     <<<---===

    6.1 find the probability that company A supplied the defective thermostat. (8)
    6.2 find the probability that company B supplied the defective thermostat. (8)
</pre>


<U>Solution</U>


<pre>
Let N be the total number of thermostats purchased from companies A, B and C.


0.7N thermostats are from company A,

0.2N thermostats are from company B, and

0.1N thermostats are from company C.


Of 0.7N thermostats from company A, 5% are defective, i.e. 0.05(0.7N) = 0.035N.

The number of all defective thermostats is 0.05*(0.7N) + 0.01*(0.2N) + 0.015*(0.1N)


Therefore, the probability that randomly selected defective thermostat came from company A is


    {{{(0.035*0.7N)/(0.05*(0.7N) + 0.01*(0.2N) + 0.015*(0.1N))}}} = {{{(0.035*0.7)/(0.05*0.7 + 0.01*0.2+0.015*0.1)}}} = 0.636364.    <U>ANSWER</U>
</pre>

Solved.


With the second question, do the same.


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Hey, why I should make corrections in your posts ?


It is your job and your responsibility to present them in ideal conditions (!)