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Six green balls and four red balls are in a bag. A ball is taken from the bag, its color recorded, then placed back in the bag. A second ball is taken and its color recorded. What is the probability the two balls are the same color?

 Jul 2, 2018
 #1
avatar+4625 
+2

There are 6 green balls and 4 red balls, making 10 total balls. The probability of picking a green ball first is 610 .

Since there are replacements, there will be still 10 balls in the bag. Now, for the second draw, you pick green again; making the probability, 510 . So, the probability of picking a green ball both times is 610510=30100=310 .

 

Next, the probability of picking a red ball is 410 . Doing the same as before, we get: 410310=325 .

 

I'm leaving the next step up to you, to solve... What can we do after this?

smileysmiley

 Jul 2, 2018
 #2
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+2

Why is the probability of a second ball 5/10 when its color is just recorded and put back in the bag? You still have 6 green balls and 4 red balls. So the second draw should still be 6/10. No?.

 Jul 2, 2018
 #3
avatar+4625 
+2

Yes, thank you, guest, forgot about that!!!

So, both are 6/10, thus 610610=925.

And for the red, 410410=425.

Thanks again, guest!

smileysmiley

tertre  Jul 2, 2018
 #4
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+1

OK, good man. Now, he says "What is the probability the two balls are the same color?" So, I think you have to add up the two probabilities together to answer his question: 9/25 + 4/25 =13/25 = 52%.

 Jul 2, 2018
edited by Guest  Jul 2, 2018

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