Question

The probability of getting a girl student selected for IAS is 0.4 and that of a boy candidate selected is 0.6. The probability that at least one of them will be selected for IAS is.......

• A. $0.76$
• B. $0.24$
• C. $1.0$
• D. $0.8$

Answer 1

The correct option is A $0.76$

$P($ getting a girl student selected $)=0.6=\frac{6}{10}$

$P($ getting a boy student selected $)=0.4=\frac{4}{10}$

$P($ a girl and a boy getting selected $)={}^n{C}_r{p}^r{q}^{n-r}$

$\Rightarrow n=2$ $p=\frac{6}{10}$ $q=\frac{4}{10}$

$\Rightarrow \frac{{}^2{C}_1{\left(\frac{6}{10}\right)}^1\left(\frac{4}{10}\right)}{2}=\frac{0.48}{2}=0.24$

$\Rightarrow P(2$ girls getting selected $)={}^2{C}_2{\left(\frac{6}{10}\right)}^2=0.16$

$\Rightarrow P(2$ boys getting selected $)={}^2{C}_2{\left(\frac{4}{10}\right)}^2=0.36$

$\Rightarrow$ Total probability $=0.24+0.16+0.36=0.76$

Hence, the answer is $\mathrm{0.76.}$