(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 times in a row. What would you do—take one side of the bet or the other, or decide not to play at all? (Your answer should depend both on your answer to the previous part of the problem and on your own personal ideas about risk and money.)(c) Answer the previous question if you are operating a casino. Compute the house advantage and 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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Unlike craps and roulette, where each throw or spin is independent of the one before it, in blackjack the probabilities for the next card depend on the cards that have been dealt so far. Since the dealer never changes his strategy, the player can overcome the house advantage by carefully counting the cards that have been dealt and betting more when his odds of winning are better. (a) What is the probability that the first card dealt will be a face card (a jack, queen or king)? (b) At what points in the deal can the probability of a face card be the same as it was at the start? (c) What is the probability that the next card dealt will be a face card if the 12 cards dealt so far have been J829K6Q9A3K4?
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.
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 have a well-mixed bowl of candy with 20 red M&Ms and 32 red Skittles, and your unsuspecting friend reaches in and scoops out 12 candies.(a) What is the probability that your friend will get exactly 10 M&Ms? (b) How many Skittles should your friend expect to get?
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
(a)Keith is playing a game on his smartphone. He will choose an image to see if he gets bonus points. The probability of getting bonus points is 8/19. Find the odds in favor of getting bonus points. (b)The manager of a restaurant determined that the odds against a customer ordering dessert are 11/2. What is the probability of a customer ordering dessert?
Please help me solve the rest.
Problem. Two players A and B, having initial amounts of money a and (t-a) dollars, respectively, play a game in which the probability that A wins a round is p and the probability that B wins is q=1-p. Each time A wins, he gets one dollar from B, otherwise he gives B one dollar. What is the probability that A will eventually get all of B's money?
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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