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There are 12 marbles in a bag, and the marbles are either yellow or green. Two marbles will be randomly picked from the bag, without replacing the first one picked. The probability that both marbles will be yellow is
5/33
How many GREEN marbles are in the bag?

Respuesta :

7 green, 5 yellow. Just worked backwards. C(12,2) = 66, so probability given is also 10/66 

If there are x yellow marbles, then C(x,2)•C(12-x,0)/C(12,2) = 10/66. Thus C(x, 2) = 10, so x = 5 = yellows. So greens = 12–5 = 7

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InesWalston

Answer:

Number of green marbles is 7.

Step-by-step explanation:

There are 12 marbles in a bag, and the marbles are either yellow or green.

Let us assume that the number yellow balls are x, so the number of green balls are 12-x.

If two marbles are drawn without replacement, the probability that both marbles will be yellow is

[tex]\dfrac{x}{12}\times \dfrac{x-1}{11}[/tex]

As we are doing the experiment without replacement, so the number of yellow marble will be 1 less than the previous as we have already drawn a yellow one. So does to the total number of marbles.

But this is give to be 33, hence

[tex]\Rightarrow \dfrac{x}{12}\times \dfrac{x-1}{11}=\dfrac{5}{33}[/tex]

[tex]\Rightarrow \dfrac{x(x-1)}{132}=\dfrac{5}{33}[/tex]

[tex]\Rightarrow \dfrac{x(x-1)}{4}=\dfrac{5}{1}[/tex]

[tex]\Rightarrow \dfrac{x(x-1)}{4}=5[/tex]

[tex]\Rightarrow x(x-1)=5\times 4[/tex]

[tex]\Rightarrow x(x-1)=20[/tex]

Solving and neglecting negative values this we get,

[tex]\Rightarrow x=5[/tex]

Therefore, number of yellow marbles is 5, number of green marbles is 7.

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