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

Sagot :

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

[tex]P(\text{Getting one 6) = }\frac{1}{6}[/tex]

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

[tex]P(\text{Not getting 6) = }\frac{5}{6}[/tex]

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

The probability of not getting 6 is given as,

[tex]P(\text{ getting atleast one 6) = 1 - P(Not getting 6)}[/tex]

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

[tex]\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}[/tex]

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