prompt: use the space below to answer the prompt. 1. hypothetical scenario: your teacher rolls a 20 - sided…

prompt: use the space below to answer the prompt. 1. hypothetical scenario: your teacher rolls a 20 - sided die. you have the opportunity to receive a specific amount of money if you correctly guess which number is rolled: guess the number exactly: $500 guess even or odd: $50 guess it will fall between 1 and 19: $5 which option would you pick and why?

prompt: use the space below to answer the prompt. 1. hypothetical scenario: your teacher rolls a 20 - sided die. you have the opportunity to receive a specific amount of money if you correctly guess which number is rolled: guess the number exactly: $500 guess even or odd: $50 guess it will fall between 1 and 19: $5 which option would you pick and why?

Answer

Explanation:

Step1: Calculate probability of exact - number guess

A 20 - sided die has 20 possible outcomes. The probability of correctly guessing the exact number is $P_{exact}=\frac{1}{20}=0.05$. The expected value of this option is $E_{exact}=500\times\frac{1}{20}= 25$.

Step2: Calculate probability of even/odd guess

There are 10 even and 10 odd numbers on a 20 - sided die. The probability of correctly guessing even or odd is $P_{even/odd}=\frac{10}{20}=0.5$. The expected value of this option is $E_{even/odd}=50\times0.5 = 25$.

Step3: Calculate probability of 1 - 19 guess

There are 19 numbers between 1 and 19 on a 20 - sided die. The probability of correctly guessing a number between 1 and 19 is $P_{1 - 19}=\frac{19}{20}=0.95$. The expected value of this option is $E_{1 - 19}=5\times0.95 = 4.75$.

Answer:

Either "Guess the number exactly" or "Guess even or odd" can be picked as they have the same expected value of 25, while the expected value of "Guess it will fall between 1 and 19" is lower at 4.75. If one is risk - averse, "Guess even or odd" might be better as it has a higher probability of winning compared to "Guess the number exactly".