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In a TV show, you must pass 3 phases to make it to the live show. From the first phase, $80$% of the people go home, the rest can continue to the second phase. From the second phase, $70$% of the people go home, those who made it this far, have to get throught the third pase, there, only $25$% of the people succeed.

There are $3$ several tasks, I wrote my ideas in each of them:

1, How many percent of the people can make it live? My idea: Let us have $X$ people in the beginning. After the first phase, only $\frac2{10}X$ people are still in. After the second phase, only $\frac3{10}*\frac2{10}X$ people are still in, and after the last phase, only $\frac14 * \frac3{10} * \frac2{10} X$ people are in, which is $\frac{3}{200}X$($1,5$% of the original)

2, There is one person, and we only know, that he made throught the first phase. What is the probability, that we will see him live? My idea: Since he made through the first phase, now he only need to make through the rest, which is $\frac{3}{10} * \frac{1}{4} = \frac{3}{40}$.

3, Examine the people, who didn't make it live. How many of them went home after the first, second and third phase? If we have $X$ people, $\frac{8}{10}X$ went home after the first phase, $\frac{2}{10}*\frac{7}{10}X$ went home after the second phase, and $\frac{2}{10}*\frac{3}{10}*\frac{3}{4}X$ went home after the last phase.

Sorry for the long task, but I am quite new to this subject. Are my approaches correct? Thanks for any help!

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    $\begingroup$ It looks OK to me. $\endgroup$ – Ian Sep 16 '15 at 11:10
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    $\begingroup$ It looks OK to me, too. $\endgroup$ – callculus Sep 16 '15 at 11:12
  • $\begingroup$ Thanks for your responses. :) $\endgroup$ – Atvin Sep 16 '15 at 11:18
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Your ans. are ok, but the last part can be greatly simplified using the concept of the complement.

% who didn't make it live $= (100 - 1.5) = 98.5$%

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Your approaches look fine too me.

If you compare your results from task 1 and 3 you can also see that the sum of all participants who go home after every stage is the complementary result of those who make it live.

While task 1 showed us $\frac{3}{200}X$ of all particpants make it live your result in task 3 showed that $$\frac{8}{10}X+\frac{2}{10}∗\frac{7}{10}X+ \frac{2}{10}∗\frac{3}{10}∗\frac34X=\frac{197}{200}X$$ particpants have to go home. Those are the other 98,5%.

Edit: This just helps to verify your assumptions here, altough task 3 asks for the percantage of people leaving after every single stage.

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