There are 3 boys and 3 Girls. An environment committee of 2 is to be formed. Write so smaple Space [5], n(s) and find the total no. of elements in the following events.
A is the event which contains at bast 2 Girls. [2 and more] .
B boys is the event which contains both the .
C ( is the event which contains Only one triangle.
D is the event which contains at most one boy [] boy or boy] ne Find the event ameaing defined above above. 1. Complementary Event 2. Mutually Exclusive event. 3. Exchaustive event
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Answer:
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Step-by-step explanation:
Committee of two is to be formed from 3 boys and 2 girls.
Let 3 boys be B
1
,B
2
,B
3
and 2 girls be G
1
,G
2
.
S={B
1
B
2
,B
1
B
3
,B
2
B
3
,G
1
G
2
,B
1
G
1
,B
1
G
2
,B
2
G
1
,B
2
G
2
,B
3
G
1
,B
3
G
2
}
∴n(S)=10
A is the event that the committee contains atleast one boy.
∴A={B
1
B
2
,B
1
B
3
,B
2
B
3
,B
1
G
1
,B
1
G
2
,B
2
G
1
,B
2
G
2
,B
3
G
1
,B
3
G
2
}
n(A)=9
∴P(A)=
n(S)
n(A)
=
10
9
and B is the event that the committee contains one boy and one girl.
∴B={B
1
G
1
,B
1
G
2
,B
2
G
1
,B
2
G
2
,B
3
G
1
,B
3
G
2
}
n(B)=6
∴P(B)=
n(S)
n(B)
=
10
6
=
5
3
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