某公园有甲、乙两个相邻景点,原拟定甲景点内有2个A班的同学和2个

某公园有甲、乙两个相邻景点,原拟定甲景点内有2个A班的同学和2个B班的同学;乙景点内有2个A班同学和3个B班同学,后由于某种原因甲、乙两景点各有一个同学交换景点观光.

(1)求甲景点恰有2个A班同学的概率;

(2)求甲景点A班同学数X的分布列及期望.

答案

解:(1)甲、乙两景点各有一个同学交换后,甲景点恰有2个A班同学有下面几种情况:

①互换的A班同学,则此时甲景点恰好有2个A班同学的事件记为A1,则P(A1)=.

②互换的是B班同学,则此时甲景点恰有2个A班同学的事件记为A2,则P(A2)=.

故P=P(A1)+P(A2)= +=.

(2)设甲景点内A班同学数为X,则X的分布列为:

X

1

2

3

P

EX=×1+×2+×3=.

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