Question

Jane's accounting department hires CPA's from three states. The head of accounting gives Jalle following information. Three states are beginning to require that future CPA's have 150 hours of college credit, VA, NC, and HI. 10% of the future CPA's will come from HI, 30% from VA, and 60% from NC. Given that a future CPA is from VA there is a 38% probability that they will have met the 150hrs of college credit requirement. Whereas, given a future CPA is from NC there is an 85% probability that they will have met the 150-hr college credit requirement. In the same vein, given a future CPA is from HI there is a 42% probability that they will have met the 150 -hr college credit requirement. The accounting department wants to know:

a. Create a joint probability table.
b. What is the probability of a future CPA not having the 150 -hr college credit requirement?
c. Given that a student does not meet the 150−hr college credit requirement, what is the probability that they are from NC?
d. Show that the state a future CPA is from and the ability to meet the 150 -hr college credit requirement are dependent events

Answer 1

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.