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