Final answer:
The correct expression to find the probability of the first success by the sixth trial in a geometric distribution with success probability of 0.12 is the complement of the probability of no successes in the first five trials, calculated as '1 - (0.88^5)' using a graphing calculator.
Step-by-step explanation:
The student is seeking to find the probability of the first success occurring by the sixth trial in a geometric distribution scenario, where the probability of success in a single event is 0.12. The correct expression to calculate this probability using a graphing calculator is by using the cumulative distribution function of the geometric distribution. In the case of calculators like the TI-83+, TI-84, you'd use the binomcdf function since the geometric distribution is a special case of the binomial distribution where the number of trials is theoretically infinite, but we are interested in the probability of the first success within a fixed number of trials.
Using the calculator, the right command would be binomcdf(6,0.12,1), which will give you the probability of at least one success in 6 trials. None of the options provided in the question (A, B, C, D) correctly represents this calculation. However, you can use the complement of the probability of no successes in the first five trials, which is equal to 1 - (0.88^5). The answer would be '1 - (the probability of failure in the first five events)' to find the probability of at least one success by the sixth event.