## anonymous 5 years ago The probability of randomly selecting a red marble from a bag, replacing it, and selecting a red marble again is 1/25. What is the probability of selecting a red marble on the first try?

1. anonymous

$\frac{1}{25}$

2. anonymous

I will become your fan and give you a medal for the right answer

3. anonymous

reason: same number of marbles in the bag the second time as the first. same number of red marbles the second time as well. so nothing has changed and the probabilities are the same.

4. anonymous

oh thanks!

5. anonymous

oh wait. i need to read the question more carefully. hold on.

6. anonymous

hold on i think i was mistaken. sorry.

7. anonymous

i misread. let me try again and this time go slow, and maybe with an explanation.

8. anonymous

ok

9. anonymous

put A = the event you select a red marble on the first try. we want $P(A)$ B = event you select a red marble on second try.

10. anonymous

$A\cap B$ is the even that both marbles selected were red, and you are given that $P(A\cap B)=\frac{1}{25}$ because you are given that the probability that both marbles selected were red

11. anonymous

in general $P(A\cap B) = P(A)\times P(B|A)$ but since you have replaced the red marble there are the same number of red marble in the bag and the same number of marbles, so $P(B)=P(A)$

12. anonymous

Shouldn't it be 1/5. 1/5 * 1/5 = 1/25 th

13. anonymous

therefore you have $\frac{1}{25}=P(A)\times P(A)$ so $P(A)=\frac{1}{5}$

14. anonymous

That is the probability of selecting it once into the same probability of it being picked again

15. anonymous

yes you are right isan_meswani. my first answer was a mistake. i read the problem incorrectly.

16. anonymous

1/5? not1/25?

17. anonymous

yes, 1/5

18. anonymous

sorry i messed you up on first try.

19. anonymous

Suppose you know there are originally 2 red marbles in the bag. How many marbles are there in all?

20. anonymous

Now this is simple, isn't it? its 10

21. anonymous

really?

22. anonymous

yes that was an easy one. $\frac{1}{5}=\frac{2}{x}$

23. anonymous

oh thanks!