GATE Mechanical Engineering (ME) 2018 Shift 1 Solved Paper

A dice is rolled 5 times
$\mathit{n}=5$
$\mathit{P}=($ Probability of getting 1)$=\frac{1}{6}$
$\mathit{q}=1-\frac{1}{6}=\frac{5}{6}$
Probability of getting 1 'at least' 4 times will include probability of getting 1- "4 times+5times"
The probability distribution is binomial distribution.
$\mathit{P}\left(\mathit{x}\ge 4\right)=\mathit{P}\left(\mathit{x}=4\right)+\mathit{P}\left(\mathit{x}=5\right)$
$={}^{\mathit{n}}{\mathit{C}}_4{\mathit{p}}^4{\mathit{q}}^{\mathit{n}-4}+{}^{\mathit{n}}{\mathit{C}}_5{\mathit{p}}^5{\mathit{q}}^{\mathit{n}-5}$
$={}^5{\mathit{C}}_4{\mathit{p}}^4{\mathit{q}}^1+{}^5{\mathit{C}}_5{\mathit{p}}^5{\mathit{q}}^0$
$=\frac{25}{{\left(6\right)}^5}+\frac{1}{{\left(6\right)}^5}=\frac{26}{{\left(6\right)}^5}=0.0033$
$\%$ probability $=0.33\%$