Deliverable 01 Worksheet 1 The First Interviewer You Meet Wi

Deliverable 01 Worksheet1 The First Interviewer You Meet With Is Ex

Deliverable 01 – Worksheet 1 involves a series of questions based on probability theory, practical scenarios involving client data, and game theory involving dice. The worksheet includes analyzing the accuracy of probability information presented by a potential client, creating probability tables for a dice game, calculating specific probabilities associated with dice outcomes, and evaluating the expected value of a game based on payouts and probabilities. Each problem requires applying basic properties of probability, combinatorial analysis, and expectation calculations to reach informed conclusions.

Paper For Above instruction

The first scenario presents a spreadsheet predicting potential client types with assigned probabilities. The client states certain probabilities, but due to the inherent randomness and limitations of estimation, this information is not perfectly accurate. Two fundamental reasons underpin this conclusion: first, probabilities in real-world settings tend to be estimates rather than exact figures. Second, the total probabilities assigned to all client types should sum to one, and if the sum of the given probabilities deviates from this, the data cannot be accurate. For example, the probabilities listed — including Corporate, Small Business, Legal, Government, and Private — must collectively total 1; if not, the data is flawed or incomplete, indicating inaccuracy. Furthermore, estimates based solely on qualitative judgment are often subject to bias or miscalculation, which undermines their precision and reliability.

Regarding the second scenario involving a dice game with two ten-sided dice numbered from 1 to 10: creating a comprehensive table of all outcomes involves listing every possible pair of results, i.e., (1,1), (1,2), ..., (10,10). Since each die has 10 faces, the total outcomes for a single roll are 10 × 10 = 100. Organizing these outcomes in a table with rows representing the result of the first die and columns representing the second die provides a clear view of all possible results and facilitates calculation of various probabilities.

For calculating the probability of rolling a sum of 11 with two ten-sided dice, we identify all outcome pairs where the sum equals 11. Valid pairs include (1,10), (2,9), (3,8), (4,7), (5,6), (6,5), (7,4), (8,3), (9,2), and (10,1), totaling 10 favorable outcomes. Since the total outcomes are 100, the probability is 10/100 = 0.10 or 10%. This calculation demonstrates the combinatorial nature of probability and the importance of systematically counting outcomes to determine likelihoods.

Next, to find the probability of rolling at least one 7 in two rolls of the dice, we can use the complement rule. First, calculate the probability of not rolling a 7 on a single die, which is 9/10. The probability that neither die shows a 7 in one roll is (9/10) × (9/10) = 81/100. Therefore, the probability of rolling at least one 7 in a single roll of two dice is 1 - 81/100 = 19/100 = 0.19 or 19%. This approach simplifies the process by avoiding explicit enumeration of all favorable outcomes containing a 7.

When calculating the probability of doubles occurring in two consecutive rolls, the first step is to determine the probability of rolling doubles in a single roll, which are the outcomes like (1,1), (2,2), ..., (10,10). There are 10 such outcomes, so the probability in one roll is 10/100 = 1/10. Assuming independence between rolls, the probability of doubles in each of two consecutive rolls is (1/10) × (1/10) = 1/100 = 0.01 or 1%. These calculations demonstrate key probability concepts such as independence and the multiplication rule.

Finally, to evaluate the expected value of the game, considering the costs and payouts, the game costs $1 to play, and the expected payout per game is $0.47. The expected value (EV) can be verified by summing the products of each payout and its associated probability. Given that the payout table is based on specific sums and outcomes, each payout’s probability is calculated by listing all outcomes that result in each sum or event, then dividing by the total number of outcomes. Confirming the expected value involves summing these products and comparing with the given $0.47 per dollar played. If the calculations match, then the assertion regarding the game's expected value is accurate; if not, discrepancies point to miscalculations or incorrect assumptions about the payouts or probabilities.

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