có hai kiện hàng I và II, mỗi kiện chứa 16 sản phẩm. số sản phẩm tốt có trong kiện I và II lần lượt là 4 và 8. từ mỗi kiện lấy ra 2 sản phẩm. tính xác suất:
a/ được 1 sản phẩm tốt, 3 sản phẩm xấu.
b/ được không quá 1 sản phẩm tốt.
lay moi kien ra 2 san pham co:$C^2_{16}.C^2_{16}=14400$ cach
$\Rightarrow |\Omega| =14400$
a) goi $A$ la` bien' co' lay ra 1 sp tot, 3 sp xau
+ lay ra sp tot o kien 1: $C^1_4.C^1_{12}.C^2_8=1344$ cach
+lay ra sp tot o kien2: $C^1_8.C^1_8.C^2_{12}=4224$ cach
$\Rightarrow $ co $1344+4224=5568$ cach lay ra 1 sp tot 3 sp xau
$\Rightarrow |\Omega _A|=5568$
Vay $P(A)=\frac{5568}{14400}=\frac{29}{75}$
b)goi $B $ la bien co khong lay duoc sp tot nao khi do $|\Omega _B|=C^2_{12}.C^2_8=1848$
vay xac suat lay ra moi kien 2 sp ma co k qua 1 san pham tot la:
$P(A\cup B)=\frac{|\Omega _A|+|\Omega _B|}{|\Omega|}=\frac{5568+1848}{14400}=\frac{103}{200}$

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