1. In a class experiment, Miguel rolls one ordinary 6-sided die repeatedly. Keeping track of each number he rolls, hedecides to stop as soon as one number is rolled three times. Miguel stops after the 12th roll, and the sum of theserolls is 47. Which number occurred for the third time? (An ordinary 6-sided die has the numbers from 1 through 6 onits sides)2. How many squares of all sizes are there on a standard 8-square by 8-square checkerboard?3. How many toothpicks will be needed to make a 7 x 7 square?

Given, *Six sided die is rolled repeatedly. *He decides to stop rolling as soon as one number{i.e…

Answered: 1. In a class experiment, Miguel rolls…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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In a certain class of 25 students, 12% received A’s, 30% received B’s, 42% received C’s, and 12% received D’s. How many students failed the class?
Ethan has a bag that contains strawberry chews, apple chews, and lime chews. He performs an experiment. Ethan randomly removes a chew from the bag, records the result, and returns the chew to the bag. Ethan performs the experiment 47 times. The results are shown below: A strawberry chew was selected 36 times. A apple chew was selected 9 times. A lime chew was selected 2 times. If the experiment is repeated 600 more times, about how many times would you expect Ethan to remove a lime chew from the bag? Round your answer to the nearest whole number.
One morning Dave an email message to Alvin that said the following: “You are one of my dearest friends. If you care about me, send a copy of this letter to two of your dearest friends tomorrow. If you do not break this chain, you will live long and prosper.” Alvin followed the directions: the next day he sent a copy of the message to two of his dearest friends. The following day, each of the recipients did the same. Count the day Dave sent the original message as the first day, and assume the chain is unbroken. A. How many copies of the message will be sent on the sixth day? B. Find the n-rule that will show how many copies of the message will sent on the n-th day.
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You need to borrow money for gas, so you ask your mother and your sister. You can only borrow money from one of them. Before giving you money, they each say they will make you play a game. Your sister says she wants you to flip a fair coin. She will give you $8$ for heads and $⁢22 for tails. Your mother says she wants you to roll a six-sided die. She will give you $4$ times the number that appears on the die. Determine the expected value of each game and decide which offer you should take.
You need to borrow money for gas, so you ask your mother and your sister. You can only borrow money from one of them. Before giving you money, they each say they will make you play a game. Your sister says she wants you to roll a six-sided die. She will give you $⁢4 times the number that appears on the die. Your mother says she wants you to spin a spinner with two outcomes, blue and red, on it. She will give you $⁢5 if the spinner lands on blue and $⁢15 if the spinner lands on red. Determine the expected value of each game and decide which offer you should take. The expected value for your sister's game: $$ The expected value for your mother's game: $$ Which offer should you take?
Imagine you draw a marble from a bag with one green, one red, one blue, and one purple marble 9 times. You replace the marble you drew every time. You record the color each time you draw. How many outcomes are possible?

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