[tex]p(x)=\lbrack\frac{n!}{x!(n-x)!}\rbrack p^x(1-p)^{n-x}[/tex][tex]\begin{gathered} In\text{ this case,} \\ p=0.623 \\ n=6 \\ x=4 \end{gathered}[/tex][tex]\begin{gathered} \text{HENCE} \\ p(4)=\lbrack\frac{6!}{4!(6-4)!}\rbrack0.623^4(1-0.623)^{6-4} \\ p(4)=\lbrack\frac{6!}{4!(2)!}\rbrack0.623^4(1-0.623)^2 \end{gathered}[/tex][tex]\begin{gathered} \\ p(4)=\lbrack\frac{720}{24\cdot2}\rbrack0.623^4(0.377)^2 \\ p(4)=\lbrack\frac{720}{48}\rbrack0.623^4(0.377)^2 \\ p(4)=\lbrack15\rbrack0.623^4(0.377)^2 \\ p(4)=\lbrack15\rbrack(0.1506)(0.1421)^{} \\ p(4)=\lbrack15\rbrack(0.1506)(0.1421) \\ p(4)=0.321 \end{gathered}[/tex][tex]\begin{gathered} \text{hence, the probability in percentage is} \\ 0.321\cdot100=32.1\text{ percent} \end{gathered}[/tex]
