GEOMETRIC DISTRIBUTIONIn an amusement fair, a competitor is entitled for a prize if he throws a ring on a pegfrom a certain distance. It is observed that only 30% of the competitors can dothis. If someone is given 5 chances, what is the probability of his winning the prizewhen he has already missed 4 chances?Determine the expected number and variance of winning in problem #44.

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Answered: 4. GEOMETRIC DISTRIBUTION In an…

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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1. For each random variable described below, give its distribution (which will be Binomial, Geometric, Hypergeometric, Pascal, or Poisson) and the parameters of that distribution. (a) You are working on a difficult homework assignment with 5 problems. Every minute, you have an idea for the problem you are working on, but it only has a 5% chance of working. If it doesn’t work, you keep working on that problem, and if it works, you move on to the next problem. The random variable W is the time (in minutes) that it takes you to finish the homework assignment. (b) A standard 52-card deck is split equally between two players. The random variable X is the number of aces received by the first player. (There are four aces in the deck.) Note: this is a key parameter when playing the “card game” “War”. (c) Every time you turn on the light, the light bulb has a 1% chance of burning out and you have to replace it. The random variable Y is the number of times you turn on the light before you have…
Problem 1. A fair coin is tossed repeatedly. Consider the following two possible outcomes: a) 55 or more heads in the first 100 tosses; b) 220 or more heads in the first 400 tosses. Without calculating, which probability is more likely? Why? Confirm this by using the normal approximation to the binomial distribution to estimate the probabilities of both events.
Problem 5: Suppose a discrete random variable X assumes the value 3/2 with probability 0.5 and assumes the value 1/2 with probability 0.5. a). Calculate the expected value and variance of X.
QUESTION 3. The state sells 5 million lottery tickets at $2.00 apiece and offers the following prizes: $100 6000 winners $2,500 250 winners $50,000 12 winners $100,000 6 winners $250,000 3 winners $2,500,000 1 winner You buy one ticket. What is the probability that your ticket wins a prize? (any prize) What is the expected value of your ticket?
Problem 5. On a distant alien planet, a full year lasts 5 days. The distribution of birthdays of the aliens who live on this planet is uniform. What is the probability that, if we randomly choose 3 aliens from this planet, at least 2 of them will have the same birthday? Explain.
Problem 1 (1) An airline finds that each passenger who reserves a seat fails to turn up with probability For an aeroplane with 18 seats, the airline sells 20 tickets. What is the probability that the flight is overbooked? (2) A cinnamon raisin bagel contains n raisins that are distributed evenly over the bagel's volume. Cut the bagel into k pieces. What is the expected number of raisins in each piece? Base your an- swer on an appropriate mathematical model!
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Please help me fix A and B problem. Thank you!

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