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An opaque bag contains 5 green marbles, 3 blue marbles, and 2 red marbles. If two consecutive marbles are drawn without replacement what is the probability that the first one will be green and the second one will be red?

 

0.51

0.10

0.11

0.16

 Oct 16, 2019
 #1
avatar+177 
+3

In total there are 5 + 3 + 2 = 10 marbles in total

The probability that the first one drawn out 5/10 = 1/2, and the chance that the second will be red is 2/9, because there is no replacement

1/2 x 2/9 = 1/9

The probability that the first one drawn out will be green and the second one is red is 1/9

 Oct 16, 2019
 #3
avatar+64 
+2

Hi Oofrence when you said that ‘the chance that the second will be red is 2/9’, is the denominator of that fraction 9 because there are 10 marbles total and a blue one was already drawn out? 

milkcloud  Oct 16, 2019
edited by milkcloud  Oct 16, 2019
edited by milkcloud  Oct 16, 2019
 #4
avatar+105664 
+2

Yes, that is why he/she said that.

Melody  Oct 16, 2019
 #5
avatar+64 
+2

@Meldody :) thanks!

milkcloud  Oct 16, 2019
edited by milkcloud  Oct 16, 2019
 #6
avatar+105664 
+2

You are welcome.

I should have let Oofrence answer for him/her self.

Sorry Oofrence.

Melody  Oct 16, 2019
edited by Melody  Oct 16, 2019
 #2
avatar+64 
+3

Not sure if this is right, but I tried writing all the possible ways and got this:

 

gg, gg, gb, gb, gb, gr, gr, bb, br, br, rr, bg, bg, bg, rb, rb

 

Each g represents a green marble, r for a red marble, and b for a blue marble

 

there are 2 green-reds (gr) and 18 possible marble color choices, which gives us 2/18 and when simplified is 1/9

 Oct 16, 2019
 #7
avatar+6045 
+1

....

.
 Oct 17, 2019
edited by Rom  Oct 18, 2019

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