Question

There are three boys and two girls. a committee of two is to be formed. find the probability of the following events

Event A : The committee contains at least one boy
Event B : The committee contains one boy and one girl
​

Answer 1

Step-by-step explanation:

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There are three boys and two girls. A committee of two is to be formed. Find the probability of the following events:

Event A: The committee contains at least one boy.

Event B: The committee contains one boy and one girl

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Solution

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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

Answer 2

Answer:

so the answer is (correct answer)

p (b)=3/5