Final answer:
The correct probability of rolling three fours in 10 rolls of a standard die is represented by the binomial expression d. 10C3(1/6)^3(5/6)^7, which signifies 10 choose 3 successes with a success probability of 1/6 and a failure probability of 5/6 for the remaining trials.
Step-by-step explanation:
The question revolves around the calculation of a specific probability problem when rolling a six-sided die 10 times. The task is to determine the probability of rolling exactly three fours out of these ten rolls.
To solve this, we apply the binomial probability formula, which is represented as: P(X=k) = nCk * (p)^k * (q)^(n-k), where:
- n represents the number of trials (in this case, 10 rolls).
- k represents the number of successful outcomes (rolling a four, in this case 3 times).
- p is the probability of success on a single trial (1/6 for rolling a four).
- q is the probability of failure on a single trial (5/6 for not rolling a four).
Therefore, the correct representation for the probability of rolling 3 fours in 10 rolls of a die is:
10C3(1/6)^3(5/6)^7
Which corresponds to option D in the question.