Question

A single die is rolled 4 times. Find the probability of getting at least one 6.

Answer 1

When a dice is rolled the probability of getting one 6 is,

$P(\text{Getting one 6) = }\frac{1}{6}$

The probability of not getting 6 when a dice is rolled is ,

$P(\text{Not getting 6) = }\frac{5}{6}$

The probability of getting 6 is independent on how many times the dice is rolled.

The probability of not getting 6 is given as,

$P(\text{ getting atleast one 6) = 1 - P(Not getting 6)}$

Therefore the probability of getting atleast one 6 when a dice is rolled 4 times is calculated as,

$\begin{gathered} P(\text{Getting 6) = 1 - (}\frac{5}{6})^4 \\ P(\text{Getting 6) = 1 - }\frac{625}{1296} \\ P(\text{Getting 6) = }0.5177 \\ \end{gathered}$

Thus the probability of getting atleast one 6 when a dice is rolled 4 times is 0.5177 .