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If a dice is rolled four times what is the probability that the same number is rolled at least twice? Round your answer to four decimal places and show your work.

Respuesta :

Answer:

[tex]\frac{171}{1296}[/tex]

Step-by-step explanation:

Let’s try to go this way.

For example the number is k. It can be of course any number. So k is between 1 to 6.

The chance of rolling exactly zero ks is: [tex](\frac{5}{6}) ^{4}[/tex]=625/1296;

The chance of rolling exactly one k is:  [tex](\frac{5}{6}) ^{3}[/tex] * [tex]\frac{4}{6}[/tex] = 500/1296;

So, the chance of rolling less than two ks is: 1125 / 1296;

So, the chance of rolling at least two ks is: 171 / 1296

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