Question

Type the correct answer in the box. Write your answer as a reduced fraction, using / for the fraction bar. A six-sided fair die is rolled 4 times in a row. The probability of getting a 4 only on the last trial is .

Answer 1

Answer:   $\bold{\dfrac{125}{1296}}$

Step-by-step explanation:

The probability of NOT getting a 4 means the probability of getting a 1, 2, 3, 5, or 6 which is 5 out of 6 = $\dfrac{5}{6}$

The probability of getting a 4 is 1 out of 6 = $\dfrac{1}{6}$

The probability of getting a 4 only on the last roll is:

NOT 4    and     NOT 4    and    NOT 4   and     Yes 4

    $\dfrac{5}{6}$           x            $\dfrac{5}{6}$            x          $\dfrac{5}{6}$           x           $\dfrac{1}{6}$      =      $\dfrac{5^3}{6^4}= \dfrac{125}{1296}$