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Question Number 199711 by Mingma last updated on 08/Nov/23

	Answered by mr W last updated on 08/Nov/23

	Commented by mr W last updated on 08/Nov/23

	$p = \frac{2 \times \frac{1}{6}}{1} = \frac{1}{3}$
	Commented by Mingma last updated on 08/Nov/23
	Perfect ��
	Answered by mr W last updated on 08/Nov/23

	$a : b =$ $1 : 3, 4, . . ., 3 n \Rightarrow 3 n - 2$ $2 : 6, 7, . . ., 3 n \Rightarrow 3 n - 5$ $3 : 9, 10, . . ., 3 n \Rightarrow 3 n - 8$ $. . .$ $n : 3 n \Rightarrow 1$ $Σ = 1 + 4 + . . . + (3 n - 2) = \frac{n (3 n - 1)}{2}$ $p = \frac{\frac{n (3 n - 1)}{2}}{C_{2}^{3 n}} = \frac{n (3 n - 1) \times 2}{2 \times 3 n (3 n - 1)} = \frac{1}{3}$
	Commented by MM42 last updated on 08/Nov/23

	$S i r W$ $^{″} b > 3 a^{″}$
	Commented by mr W last updated on 08/Nov/23

	$y o u a r e r i g h t s i r!$ $i p u r p o s e l y t o o k b ⩾ 3 a i n o r d e r t o g e t$ $p = \frac{1}{3} i n d e p e n d e n t l y f r o m n .$
	Answered by MM42 last updated on 08/Nov/23
	$b> 3a a=1→b=4,5,6,..,3n ⇒m_1 =3n−3 a=2→b=7,8,9,...,3n⇒m_2 =3n−6 ⋮ a=n−1→b=3n−2,3n−1,3n⇒m_(n−1) =3 n(A)=3+6+...+(3n−3)=((3n(n−1))/2) n(S)= (((3n)),(( 2)) )=((3n(3n−1))/2) ⇒ p(A)=((n−1)/(3n−1)) ✓ for example : n=3 : 1,2,..,9⇒n(S)= ((9),(2) )=36 A={{1,4},{1,5},...,{1,9},{2,7},{2,8},{2,9}}⇒n(A)=9 ⇒p(A)=(1/4) ✓$
	$b > 3 a$ $a = 1 \to b = 4, 5, 6, . ., 3 n \Rightarrow m_{1} = 3 n - 3$ $a = 2 \to b = 7, 8, 9, . . ., 3 n \Rightarrow m_{2} = 3 n - 6$ $⋮$ $a = n - 1 \to b = 3 n - 2, 3 n - 1, 3 n \Rightarrow m_{n - 1} = 3$ $n (A) = 3 + 6 + . . . + (3 n - 3) = \frac{3 n (n - 1)}{2}$ $n (S) = (\begin{matrix} 3 n \\ 2 \end{matrix}) = \frac{3 n (3 n - 1)}{2}$ $\Rightarrow p (A) = \frac{n - 1}{3 n - 1} ✓$ $f o r e x a m p l e :$ $n = 3 : 1, 2, . ., 9 \Rightarrow n (S) = (\begin{matrix} 9 \\ 2 \end{matrix}) = 36$ $A = {{1, 4}, {1, 5}, . . ., {1, 9}, {2, 7}, {2, 8}, {2, 9}} \Rightarrow n (A) = 9$ $\Rightarrow p (A) = \frac{1}{4} ✓$
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