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Question Number 209036 by Tawa11 last updated on 30/Jun/24
There are 5 people in a school, 2 boys and 3girls,  two students, are chosen at random, find the  probability of choosing two different sexes.
There are 5 people in a school, 2 boys and 3girls,
two students, are chosen at random, find the
probability of choosing two different sexes.
Commented by Tawa11 last updated on 30/Jun/24
Is the answer  (3/5)  or  (3/(25))?
$$\mathrm{Is}\:\mathrm{the}\:\mathrm{answer}\:\:\frac{\mathrm{3}}{\mathrm{5}}\:\:\mathrm{or}\:\:\frac{\mathrm{3}}{\mathrm{25}}? \\ $$
Answered by A5T last updated on 30/Jun/24
I: b_1 b_2  − 1  g_1 g_2 ;g_2 g_3 ;g_1 g_3   −3  b_1 g_1 ;b_1 g_2 ;b_1 g_3 ;b_2 g_1 ;b_2 g_2 ;b_2 g_3  − 6  ⇒P=(6/(10))=(3/5)    II: 2×3=6 ways to choose a boy and a girl  ^5 C_2 =10 ways to choose 2 people  ⇒P=(6/(10))=(3/5)
$${I}:\:{b}_{\mathrm{1}} {b}_{\mathrm{2}} \:−\:\mathrm{1} \\ $$$${g}_{\mathrm{1}} {g}_{\mathrm{2}} ;{g}_{\mathrm{2}} {g}_{\mathrm{3}} ;{g}_{\mathrm{1}} {g}_{\mathrm{3}} \:\:−\mathrm{3} \\ $$$${b}_{\mathrm{1}} {g}_{\mathrm{1}} ;{b}_{\mathrm{1}} {g}_{\mathrm{2}} ;{b}_{\mathrm{1}} {g}_{\mathrm{3}} ;{b}_{\mathrm{2}} {g}_{\mathrm{1}} ;{b}_{\mathrm{2}} {g}_{\mathrm{2}} ;{b}_{\mathrm{2}} {g}_{\mathrm{3}} \:−\:\mathrm{6} \\ $$$$\Rightarrow{P}=\frac{\mathrm{6}}{\mathrm{10}}=\frac{\mathrm{3}}{\mathrm{5}} \\ $$$$ \\ $$$${II}:\:\mathrm{2}×\mathrm{3}=\mathrm{6}\:{ways}\:{to}\:{choose}\:{a}\:{boy}\:{and}\:{a}\:{girl} \\ $$$$\:^{\mathrm{5}} {C}_{\mathrm{2}} =\mathrm{10}\:{ways}\:{to}\:{choose}\:\mathrm{2}\:{people} \\ $$$$\Rightarrow{P}=\frac{\mathrm{6}}{\mathrm{10}}=\frac{\mathrm{3}}{\mathrm{5}} \\ $$
Commented by Tawa11 last updated on 30/Jun/24
Thanks sir.
$$\mathrm{Thanks}\:\mathrm{sir}. \\ $$

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