anonymous
  • anonymous
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?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\frac{1}{25}\]
anonymous
  • anonymous
I will become your fan and give you a medal for the right answer
anonymous
  • 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.

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anonymous
  • anonymous
oh thanks!
anonymous
  • anonymous
oh wait. i need to read the question more carefully. hold on.
anonymous
  • anonymous
hold on i think i was mistaken. sorry.
anonymous
  • anonymous
i misread. let me try again and this time go slow, and maybe with an explanation.
anonymous
  • anonymous
ok
anonymous
  • 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.
anonymous
  • 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
anonymous
  • 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 \[P(B)=P(A)\]
anonymous
  • anonymous
Shouldn't it be 1/5. 1/5 * 1/5 = 1/25 th
anonymous
  • anonymous
therefore you have \[\frac{1}{25}=P(A)\times P(A)\] so \[P(A)=\frac{1}{5}\]
anonymous
  • anonymous
That is the probability of selecting it once into the same probability of it being picked again
anonymous
  • anonymous
yes you are right isan_meswani. my first answer was a mistake. i read the problem incorrectly.
anonymous
  • anonymous
1/5? not1/25?
anonymous
  • anonymous
yes, 1/5
anonymous
  • anonymous
sorry i messed you up on first try.
anonymous
  • anonymous
Suppose you know there are originally 2 red marbles in the bag. How many marbles are there in all?
anonymous
  • anonymous
Now this is simple, isn't it? its 10
anonymous
  • anonymous
really?
anonymous
  • anonymous
yes that was an easy one. \[\frac{1}{5}=\frac{2}{x}\]
anonymous
  • anonymous
oh thanks!

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