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) = }(1)/(6)`

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

`P(\text{Not getting 6) = }(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 - (}(5)/(6))^4 \\ P(\text{Getting 6) = 1 - }(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 .