甲、乙、丙3人投篮,投进的概率分别是 2 5 , 1 2 , 1 3 .现3人各投

2025-06-27 19:28:52
推荐回答(1个)
回答1:

(Ⅰ)记“甲投进“为事件A 1 ,“乙投进“为事件A 2 ,“丙投进“为事件A 3
则P(A 1 )=
2
5
,P(A 2 )=
1
2
,P(A 3 )=
1
3

∴P(A 1 A 2 A 3 )=P(A 1 )?P(A 2 )?P(A 3 )=
2
5
×
1
2
×
1
3
=
1
15

∴3人都投进的概率为
1
15

(Ⅱ)设“3人中恰有2人投进“为事件B
P(B)=P(
.
A 1
A 2 A 3 )+P(A 1
.
A 2
A 3 )+P(A 1 A 2
.
A 3

=P(
.
A 1
)?P(A 2 )?P(A 3 )+P(A 1 )?P(
.
A 2
)?P(A 3 )+P(A 1 )?P(A 2 )?P(
.
A 3

=(1-
2
5
)×
1
2
×
1
3
+
2
5
×(1-
1
2
)×
1
3
+
2
5
×
1
2
×(1-
1
3
)=
3
10

∴3人中恰有2人投进的概率为
3
10