(a) What is the probability that a fair coin lands tails up eight times in a row?(b) Suppose you're offered a bet at 250:1 odds against a fair coin landing tails up eight timesin a row. What would you do-take one side of the bet or the other, or decide not to play atall? (Your answer should depend both on your answer to the previous part of the problemand on your own personal ideas about risk and money.)(c) Answer the previous question if you are operating a casino. Compute the house advantageand explain how much money you would make in the long run.(d) Which is more likely, that eight flips will be TTTTTTTT or that they will be THTHTHTH?

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Answered: (a) What is the probability that a fair…

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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part ii
Consider the following game. You are to toss three fair coins. If three heads turn up, your friend pays you $40. Otherwise, you must pay him $5. What is your expected gain or loss? 0.525 a. 0.625 Ob. 0.875 C. Od. 1235 0.125 Oe.
c) A manufacturer is considering the production of a new and better mousetrap. She estimates the probability that the new mousetrap is successful is ¾. If it is successful, it would generate profits of $174,000. The development costs of the mousetrap are $121,000. Should the manufacturer proceed with plans for the new mousetrap? Why or why not?
two fair coins. He wins $5 if 2 heads occur, $2 if Problem#6: A player tosses 1head occurs and $1 if no heads occur. (i) Find his expected winnings. (ii) How much should he pay to play the game if it is to be fair?
You are planning a three-day trip to Seattle, Washington, in October. Use the fact that on each day, it could be either sunny or rainy. What is the probability that it is sunny all three days? What is the probability that it rains on exactly one day?
Charlie buys a one-year term home insurance policy for $p, that will pay $200,000 in the event of a major catastrophe and $35,000 in the event of a minor catastrophe. Charlie's home has a 0.2% chance of a major catastrophe and a 0.7% of a minor catastrophe during the one year term. What did the insurance company charge Charlie for this policy if the company expected to break even?
You purchase a brand new car for $15,000 and insure it. The policy pays 78% of the car's value if there is an issue with the engine or 30% of the car's value if there is an issue with the speaker system. The probability of an issue with the engine is 0.009, and the probability there is an issue with the speaker system is 0.02. The premium for the policy is p. Let X be the insurance company's net gain from this policy. (a) Create a probability distribution for X, using p to represent the premium on the policy. Enter the possible values of X in ascending order from left to right. P(X) (b) Compute the minimum amount the insurance company will charge for this policy. Round your answer to the nearest cent
You flip two fair coins. If both coins land heads you win $2. Otherwise you lose $1. What is the expectation of this game? Round your answer to the nearest cent.
Please help me solve the rest.
You pay $3.50 to play the following game:Each of two fair dice are numbered with 3 on one side, a 2 on two sides, and a 1 on three sides.The dice are rolled once and you are returned the dollar amount corresponding to the sum on thefaces. What is the expected earning from the game?
Suppose it costs $29 to roll a pair of dice. You get paid 4 dollars times the sum of the numbers that appear on the dice. What is the expected payoff of the game? Is it a fair game? The expected payoff of the game is $? is it a fair game?
Diane has decided to play the following game of chance. She places a $1 bet on each repeated play of the game in which the probability of her winning $1 is .4. She has further decided to continue playing the game until she has either accumulated a total of $3 or has lost all her money. What is the probability that Diane will eventually leave the game a winner if she started with a capital of $1? Of $2? capital of $1 capital of $2

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