Question 6.0 - Bernoulli Trials binompdf and binomcdf (calculator)Please solve the problem with simple probability rules ### Probability Concepts in Multiple Choice Exams**Example Scenario:**Stat A. Stishen is a Business Statistics student at State U. Unfortunately, he is not a very mature student and he shows up for the final exam having spent no time preparing for it. During the multiple-choice (MC) portion of the exam, he simply uses the random integer command on his calculator to make guesses for each item. Each item has five possible choices (only one is correct). The items referenced below only refer to this portion of the exam.**Questions:**(a) **What is the probability that Stat’s first correct response is on the third item?**To solve this, we assume Stat guesses randomly for each item with each having an equal probability. Since each item has five choices, the probability of guessing correctly is:\[ P(\text{Correct}) = \frac{1}{5} \]Conversely, the probability of guessing incorrectly is:\[ P(\text{Incorrect}) = \frac{4}{5} \]For the first correct response to be on the third item, Stat must guess incorrectly on the first two items and correctly on the third:\[ P( \text{First correct on third item} ) = \left( \frac{4}{5} \right)^2 \times \left( \frac{1}{5} \right) \]So:\[ P( \text{First correct on third item} ) = \frac{16}{25} \times \frac{1}{5} = \frac{16}{125} = 0.128 \](b) **What is the probability it takes at least 8 items for Stat’s first correct response?**This implies Stat guesses incorrectly the first 7 times, then either guesses correctly on the 8th item or even later. The probability of guessing incorrectly 7 times consecutively is:\[ P(\text{Incorrect 7 times}) = \left( \frac{4}{5} \right)^7 \]So:\[ P(\text{At least 8 items}) = \left( \frac{4}{5} \right)^7 \]Calculating this:\[ P(\text{At least 8 items}) = \left( \frac{4}{5} \right)^7 \approx 0.209 \](c) **How many items do we expect Stat to answer before his first correct response? Interpret

In the final exam, the multiple choice portion of exam, he solve one question and has five possible…

6. Stat A. Stishen is a Business Statistics student at State U. Unfortunately, he is not a very mature student, and he shows up for the final exam having spent no time preparing for it. During the multiple choice (MC) portion of the exam, he simply uses the random integer command on his calculator to make guesses for each item. Each item has five possible choices (only one is correct). The items referenced below only refer to this portion of the exam. (a) What is the probability Stat's first correct response is on the third item? (b) What is the probability it takes at least 8 items for Stat's first correct response? (c) How many items do we expect Stat to answer before his first correct response? Interpret the result

6. Stat A. Stishen is a Business Statistics student at State U. Unfortunately, he is not a very mature student, and he shows up for the final exam having spent no time preparing for it. During the multiple choice (MC) portion of the exam, he simply uses the random integer command on his calculator to make guesses for each item. Each item has five possible choices (only one is correct). The items referenced below only refer to this portion of the exam. (a) What is the probability Stat's first correct response is on the third item? (b) What is the probability it takes at least 8 items for Stat's first correct response? (c) How many items do we expect Stat to answer before his first correct response? Interpret the result

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter14: Counting And Probability

Section14.FOM: Focus On Modeling: The Monte Carlo Method

Problem 3P: Dividing a JackpotA game between two players consists of tossing a coin. Player A gets a point if...

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