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A six-sided fair die is rolled 4 times in a row. The probability of getting a 4 only on the last trial is

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semsee45

Answer:

\(\dfrac{125}{1296}\)

Step-by-step explanation:

To find the probability of getting a 4 only on the last trial when rolling a fair six-sided die four times in a row, we can analyse each roll independently.

Since the die is fair, each outcome has an equal probability of 1/6.

The probability of not getting a 4 on one roll is the sum of the probability of rolling each of the other numbers:

\(\sf P(1\;or\;2\;or\;3\;or\;5\;or\;6)=\dfrac{1}{6}+\dfrac{1}{6}+\dfrac{1}{6}+\dfrac{1}{6}+\dfrac{1}{6}=\dfrac{5}{6}\)

The probability of getting a 4 on one roll is:

\(\sf P(4)=\dfrac{1}{6}\)

To find the probability of getting a 4 only on the last trial, we multiply the probability of not getting a 4 on the first three trials by the probability of getting a 4 on the last trial:

\(\sf P(4\;on\;last\;trial\;only)=\dfrac{5}{6}\times \dfrac{5}{6}\times \dfrac{5}{6}\times \dfrac{1}{6}=\dfrac{125}{1296}\)

So, the probability of getting a 4 only on the last trial is:

\(\LARGE\boxed{\boxed{\dfrac{125}{1296}}}\)

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