name: \nprompt: use the space below to answer the prompt. 1. hypothetical scenario: your teacher rolls a 20…

name: \nprompt: 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?

name: \nprompt: 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 guessing exactly

The probability of guessing exactly one number on a 20 - sided die is $\frac{1}{20}$ since there is 1 correct number out of 20 possible outcomes.

Step2: Calculate probability of guessing even or odd

There are 10 even and 10 odd numbers on a 20 - sided die. So the probability of guessing even or odd correctly is $\frac{10}{20}=\frac{1}{2}$.

Step3: Calculate probability of guessing between 1 and 19

There are 19 numbers between 1 and 19 out of 20 possible outcomes. So the probability is $\frac{19}{20}$.

Step4: Calculate expected value for each option

  • For guessing exactly: Expected value $E_1 = 500\times\frac{1}{20}= 25$.
  • For guessing even or odd: Expected value $E_2=50\times\frac{1}{2}=25$.
  • For guessing between 1 and 19: Expected value $E_3 = 5\times\frac{19}{20}=4.75$.

Answer:

The best option is to guess even or odd or to guess the number exactly as they have the same expected value of 25, and the probability of guessing even or odd is higher than guessing the exact number which might make it a more appealing choice in terms of having a higher - chance of winning something.