Question

There are three boys and two girls. A committee of two is to be formed, Find the probability of events that the committee contains only Boys


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Answer 1

Answer:

Committee of two is to be formed from 3 boys and 2 girls.

Let 3 boys be B1,B2,B3 and 2 girls be G1,G2.

S={B1B2,B1B3,B2B3,G1G2,B1G1,B1G2,B2G1,B2G2,B3G1,B3G2}

∴n(S)=10

A is the event that the committee contains atleast one boy.

∴A={B1B2,B1B3,B2B3,B1

Answer 2

Answer:

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

Step-by-step explanation:

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