Deliverable 01 Worksheet 1 The First Interviewer You 964837
Deliverable 01 Worksheet1 The First Interviewer You Meet With Is Ex
Deliverable 01 – Worksheet 1. The first interviewer you meet with is explaining to you the importance of knowing the regional business landscape in order to be best prepared for new potential clients. She shows you a spreadsheet predicting potential client types with the following information. Using basic properties of probabilities, state two reasons how you know this information is not accurate. Client Type Corporate Small Business Legal Government Private Probability 0.....7 Enter your step-by-step answer and explanations here.
The second interviewer presents a scenario involving a dice game with two 10-sided dice numbered 1 through 10. The task is to create a table showing all possible outcomes of one roll, determine the probability of specific outcomes such as rolling a sum of 11, rolling at least one 7, and rolling doubles twice in a row. Additionally, the interviewer mentions the game's expected value of 47 cents per dollar played and asks to verify this based on provided payout information. The objective is to analyze the probability distributions and expected value thoroughly.
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The first scenario involves a critical evaluation of a probability forecast related to potential clients in various sectors. The provided data shows a predicted probability distribution across different client types, with the sum apparently not equaling 1 or being inconsistent. Two key reasons to suspect inaccuracy in this information are as follows: Firstly, the total probability must sum to 1, as it encompasses all possible mutually exclusive events. If the probabilities listed — starting with 0 and ending with 0.7, for example — do not total to 1, this indicates an error in the data. For instance, if the sum of all client type probabilities is less than 1, it implies that some potential client types are missing or unaccounted for. Secondly, probabilities must be between 0 and 1 inclusive. If any individual predicted probability exceeds 1 or is negative, it violates the fundamental properties of probability, rendering the data invalid. For example, if '0.....7' is intended to be '0.7' but is misrepresented or if other probabilities such as the sum of all client types are improperly calculated, the data cannot be trusted.
In the second scenario, the game involves rolling two 10-sided dice, each numbered from 1 through 10. To understand the possible outcomes, a comprehensive table of all 100 outcome combinations can be constructed by pairing each face of the first die with each face of the second die. This table enables calculating probabilities of specific events. For example, to determine the probability of rolling a sum of 11, one counts the number of outcome pairs that sum to 11 (such as (1,10), (2,9), (3,8), (4,7), (5,6), (6,5), (7,4), (8,3), (9,2), (10,1)). Since there are 10 such pairs, the probability is the number of favorable outcomes divided by 100 total outcomes, that is 10/100 = 0.10 or 10%. Similarly, to find the probability of rolling at least one 7, identify all pairs where either die shows a 7, then count these outcomes. The probability of rolling doubles twice in a row involves independent probability calculations: the chance of rolling doubles (both dice showing the same number) once is 10/100 (since there are 10 doubles in total: (1,1), (2,2), ..., (10,10)). The probability of this happening twice consecutively is the product of their individual probabilities: (10/100) * (10/100) = 1/100 or 1%.
The expected value (EV) of the game per dollar spent is derived by multiplying each outcome's payout by its probability, then summing these products. Given the payouts for various sums and doubles, and the initial cost of $1, the calculation involves first determining the probability of each event, then applying the payout amounts. For example, the probability of rolling a sum of 19 with two 10-sided dice (though impossible, as the maximum sum is 20), highlights the importance of verifying the probability distribution. Based on the data, the EV is claimed to be 47 cents per dollar, which can be validated by summing the weighted payouts across all outcomes. If the computed EV aligns with this figure, the assertion is valid; otherwise, the calculation or assumption about the payouts may be flawed. This comprehensive analysis underscores the importance of probability theory in evaluating game fairness and profitability.
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