Matt has lots of experience taking multiplechoice exams without doing much studying. He is about to take a quiz that has10

10multiplechoice questions, each with four possible answers. Here is Matt's personal probability model.

He thinks that in75%

75%of questions, he can eliminate one answer as obviously wrong; then he guesses from the remaining three. He then has probability1

1in3

3of guessing the right answer.

For the other25%

25%of questions, he must guess from all four answers, with probability1

1in4

4of guessingcorrectly.

Make a tree diagram for the outcome of a single question. To conduct the simulation of a10

10question quiz, assign random digits asshown.

Stage1

1:

• Let the digits00
• 00to74
• 74represent the 75% of questions that Matt can eliminate one answer choice as obviouslywrong.
• Let the digits75
• 75to99
• 99represent the 25% of questions that Matt cannot eliminate an answerchoice.

Stage2

2when Matt can eliminate one answer choice as obviouslywrong:

• Let the digits00
• 00to32
• 32represent a correct answerchoice.
• Let the digits33
• 33to99
• 99represent an incorrect answerchoice.

Stage2

2when Matt must guess from all fouranswers:

• Let the digits00
• 00to24
• 24represent a correct answerchoice.
• Let the digits25
• 25to99
• 99represent an incorrect answerchoice.

Questions are independent. To simulate the quiz, simulate10

10questions starting on line119

119fromTable A. Matt needs to get at least six questions right to pass the quiz.

Estimate the number of questions Matt gets correct using the results from thesimulation.

Matt's score: