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

P = Number of ways of getting only 4 at the last trial / Total number of waysNumber of ways of getting only 4 at the last trial = 5 * 5 * 5 * 1 = 125 (for the first three trials, all but 4 is permissible (6 - 1 = 5 ways), and for the last trial, only 4 is permissible (1 way)).Total number of ways = 6 * 6 * 6 * 6 = 1296.P = 125/1296.

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MrRoyal MrRoyal · Answer 2 · 2022-05-18T11:13:20+02:00

The probability of getting a 4 only on the last trial is 125/1296

How to determine the probability?

The sample space of a fair die is;

S = {1,2,3,4,5,6}

This means that the probability of obtaining a 4 is:

P(4) = 1/6

The probability of not obtaining a is:

P(not 4) =5/6

The probability of getting a 4 only on the last trial is calculated as:

P = P(not 4) * P(not 4) * P(not 4) * P(4)

So, we have:

P =5/6 * 5/6 * 5/6 * 1/6

Evaluate

P = 125/1296

Hence, the probability of getting a 4 only on the last trial is 125/1296