Question

A six-faced fair dice is rolled five times. The probability (in %) of obtaining "ONE" at least four times is

• A. 33.3
• B. 3.33
• C. 0.33
• D. 0.0033

Answer 1

The correct option is C 0.33

Probability of getting 1 in single throw
$P=\left(\frac{1}{6}\right)$

and not getting 1 is
$q=1-\frac{1}{6}=\left(\frac{5}{6}\right)$

$\Rightarrow$ Now probability of getting 1 atleast 4 times in 5 times rolled

Here n = 5

$P(x\ge 4)={}^n{C}_4\left(P{)}^4\right(q{)}^{n-4}+{}^n{C}_5\left(P{)}^5\right(q{)}^{n-5}$

$\Rightarrow P(x\ge 4)={(}^5{C}_4\left)\right(1/6{)}^4(5/6{)}^1+{}^5{C}_5{\left(\frac{1}{6}\right)}^5{\left(\frac{5}{6}\right)}^0$

$=5\times {\left(\frac{1}{6}\right)}^4\left(\frac{5}{6}\right)+\left(1\right){\left(\frac{1}{6}\right)}^5$

$=3.343\times {10}^{-3}$

Now % $=3.343\times {10}^{-3}\times 100=0.33$