QR question

[299678]

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1. A bag contains 2 yellow, 6 green and 2 blue billiard balls. Of the 6 balls picked at random without replacement, what is the probability all 3 colors in equal number?

answer is 1/14

Need your reasoning. Thank you

2. if f[g(x)] = (x+1)^2 and g(x) = x^2
find f(x) when x = 4,

answer is 9

I need explanation for this problem

 

[Streetwolf]

1. A bag contains 2 yellow, 6 green and 2 blue billiard balls. Of the 6 balls picked at random without replacement, what is the probability all 3 colors in equal number?

answer is 1/14

Need your reasoning. Thank you

2. if f[g(x)] = (x+1)^2 and g(x) = x^2
find f(x) when x = 4,

answer is 9

I need explanation for this problem

1. With 6 balls picked it has to be 2-2-2.

(2 C 2) * (2 C 2) * (6 C 2) / (10 C 6)

Choose the 2 yellow balls * choose the 2 blue balls * choose the 2 green balls all divided by choose the 6 balls total that you can draw.

1 * 1 * 15 / 210 = 15/210 = 5/70 = 1/14

2. It wants f(x) when x = 4, so f(4) means g(x) = 4 since you had f(g(x)). This happens when the x in g(x) = 2 since (2)^2 = 4. In other words if the x in g(x) were 2 then g(2) = 2^2 = 4 and now you have your f(4). Since you now know the original x is 2, you can continue by doing (2 + 1)^2 = 9 and that's your answer. f(4) = 9.