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## anonymous one year ago There are 6 red marbles, 9 blue marbles, and 10 green marbles in a bag. What is the theoretical probability of randomly drawing a red marble and then a green marble?

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1. anonymous

depends entirely on whether you replace the marble or not after the first one is drawn

2. anonymous

The first one is not replaced.

3. anonymous

oh wait NOT replaced lets go slow

4. anonymous

what is the probability the first one is red?

5. anonymous

i hope that is more or less obvious it is the ratio of the number or red marbles to the total number of marbles

6. anonymous

24%?

7. anonymous

There are 4 answers: 10% 9.6% 16% 64%

8. anonymous

not really interested in percents before we compute these numbers we need fractions first, then we can turn the final answer in to a percent

9. anonymous

$\frac{ 24 }{100}?$

10. anonymous

lets go slow how many red marbles are there?

11. anonymous

6

12. anonymous

yes, and how many marbles are there total?

13. anonymous

25

14. anonymous

right so the probability of picking a red marble first is $\frac{6}{25}$

15. anonymous

now the red marble is chosen, and apparently not replaced how many green marbles are there ?

16. anonymous

10

17. anonymous

and how many marbles are left in the bag?

18. anonymous

24

19. anonymous

so the probability of picking a green marble once one red one is removes is?

20. anonymous

$\frac{ 10 }{ 24 }$?

21. anonymous

yes

22. anonymous

to compute the probability that both things occur, multiply

23. anonymous

$\frac{6}{25}\times \frac{10}{24}$

24. anonymous

$\frac{ 60 }{ 600 }$

25. anonymous

better known on planet earth as $$\frac{1}{10}$$

26. anonymous

or $$0.1$$ or even $$10\%$$

27. anonymous

So that's the answer?

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