Question

a class consist of 9 boys and girls. four students from this class are to be selected randomly to represent their class in a debate competition. find probability that this group consist of (i) 3 boys and 1 girl (ii) 2 boys and 2 girls (iii) 1 boy and 3 girls

Answer 1

Given :  A class consists of 9 B and G

Four students from this class are to be selected randomly to represent their class in a debate competition.

To  Find  : the Probability that this group consists of

(i) 3 B and 1 G, (ii) 2 B and 2 G (iii) 1 B and 3 G

Solution:

Number of G not given :

Let say G are also 9

Then total = 18

4 out of 18 can be selected in  ¹⁸C₄  =   3,060  

3 B and 1 G   can be selected  in  ⁹C₃*⁹C₁ =  756

Probability = 756/3060  =  21/85 = 0.247

2 B and 2 G   can be selected  in  ⁹C₂*⁹C₂ =  1296

Probability =1296/3060  =36/85 = 0.4235

1 B  and 3 G   can be selected  in  ⁹C₁*⁹C₃ =  756

Probability = 756/3060  =  21/85 = 0.247

If G assume d   x

Then total = 9 + x

4 out of 9 + x can be selected in  ⁹⁺ˣC₄  

3 B and 1 G  can be selected  in  ⁹C₃*ˣC₁  

Probability =  ⁹C₃*ˣC₁   / ⁹⁺ˣC₄  

2 B and 2 G  can be selected  in  ⁹⁺ˣC₂*ˣC₂  

Probability = ⁹⁺ˣC₂*ˣC₂   / ⁹⁺ˣC₄  

1 B  and 3 G   can be selected  in  ⁹C₁*ˣC₃  

Probability = ⁹C₁*ˣC₃  / ⁹⁺ˣC₄

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