某旅游地有甲乙两个相邻景点,甲景点内有2个美国旅游团和两个日本旅游团,乙景点内有2个美国旅游团和3个日本旅游团,现甲乙两

解题思路：（I）互换后甲景点恰有2个美国旅游团，说明交换的是相同的团：都是美国旅游团或都是日本旅游团，从而可求出所求；
（II）互换后甲景点内美国旅游团数可能为1、2、3，然后分别求出相应的概率，最后利用数学期望公式解之即可．

（Ⅰ）甲乙两个景点各有一个外国旅游团交换后，甲景点恰有2个美国旅游团有下面几
种情况：①都交换的是美国旅游团，则此时甲景点恰有2个美国旅游团事件A₁的概率P(A1)＝

C12
C12

C14
C15＝
1
5．…（2分）②都交换的是日本旅游团，则此时甲景点恰有2个美国
旅游团事件A₂的概率 P(A2)＝

C12
C13

C14
C15＝
3
10．…（4分）
故P（A）=P（A₁）+P（A₂）=[1/5+
3
10＝
1
2]．…（6分）
（Ⅱ）设甲景点内美国旅游团数为ξ，则ξ的分布列为：…（7分）

ξ 1 2 3
P [3/10] [1/2] [1/5]Eξ＝
3
10×1+
1
2×2+
1
5×3＝
19
10．…（12分）

点评：
本题考点： 离散型随机变量的期望与方差；古典概型及其概率计算公式．

考点点评： 本题主要考查学生的思维能力，互换后甲景点恰有2个美国旅游团，要明确交换的是同一种团是解题的关键，属于基础题．

（Ⅰ）甲乙两个景点各有一个外国旅游团交换后，甲景点恰有2个美国旅游团有下面几
种情况：①都交换的是美国旅游团，则此时甲景点恰有2个美国旅游团事件A ₁ 的概率 P( A 1 )=

C 12
C 12

C 14
C 15 =
1
5 ．…（2分）②都交换的是日本旅游团，则此时甲景点恰有2个美国
旅游团事件A ₂ 的概率 P( A 2 )=

C 12
C 13

C 14
C 15 =
3
10 ．…（4分）
故P（A）=P（A ₁ ）+P（A ₂ ）=
1
5 +
3
10 =
1
2 ．…（6分）
（Ⅱ）设甲景点内美国旅游团数为ξ，则ξ的分布列为：…（7分）

ξ 1 2 3
P
3
10
1
2
1
5 Eξ=
3
10 ×1+
1
2 ×2+
1
5 ×3=
19
10 ．…（12分）

除掉甲乙两个风景剩6个
就是 2个风景选一个,6个风景选一个
2*6=12

D

The Whites are going to visit Xiamen for vacation. They are staying for a week. They plan to go swimming in the sea and eat delicious seafood and Xiamen food. They hope to make some friends there. Xiamen is very beautiful and the weather is good, too. The Whites will have a relaxing and happy vacation there.

Last winter holiday, I went to Harbin with my mother.
It's very cold in winter. There is snow and ice everywhere and you are always in a white world. You must wear warm clothes. The most exciting thing is playing with snow. Skating is also very interesting there.
I will' always remember Harbin, for the snow, the ice and all the beautiful things. I love Harbin

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设原路返回时需要x小时,依题意
90：x=100:6
x=4.5

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是8C2-6C2,8C2指的是在八个景区中任选2个,6C2指的是在除甲景区和乙景区外的六个景区中任选2个,这一部分是不满足甲乙景区必选一个以上要求的,抽屉原理

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(1)13种(2)27种(3)12种

（1）13种
（2）12+15=27种
（3）12种

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