Answer :
Answer:
[tex]\dfrac{125}{1296}[/tex]
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:
[tex]\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}[/tex]
The probability of getting a 4 on one roll is:
[tex]\sf P(4)=\dfrac{1}{6}[/tex]
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:
[tex]\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}[/tex]
So, the probability of getting a 4 only on the last trial is:
[tex]\LARGE\boxed{\boxed{\dfrac{125}{1296}}}[/tex]
