Final answer:
A joint probability table was created to show the probabilities of future CPAs from different states meeting the 150-hr credit requirement. From the table, it was calculated that the probability of a future CPA not meeting the requirement is 33.4%. The probability that a student is from NC given they did not meet the requirement is approximately 26.95%, and state and meeting the requirement are shown to be dependent events.
Step-by-step explanation:
We will create a joint probability table to answer the scenario described.
StateMeet 150 hours (%)Does not meet 150 hours (%)TotalHI10% * 42% = 4.2%10% * 58% = 5.8%10%VA30% * 38% = 11.4%30% * 62% = 18.6%30%NC60% * 85% = 51%60% * 15% = 9%60%Total66.6%33.4%100%
b. The probability of a future CPA not having the 150-hr college credit requirement is the sum of the individual probabilities of not meeting the requirement from the three states, which is 5.8% + 18.6% + 9% = 33.4%.
c. To find the probability that a student is from NC given they do not meet the requirement, we apply Bayes' theorem. The probability is (9% / 33.4%) which is approximately 26.95%.
d. To show that the state a future CPA is from and meeting the 150-hr college credit requirement are dependent events, we can show that the probability of both occurring is not equal to the product of their independent probabilities. For instance, the joint probability for HI is 4.2%, but if they were independent, it would be 10% * the overall probability of meeting the requirement (66.6%), which doesn't equal 4.2%, thus proving dependence.