On 3A lucky draw involves rolling a six-sided dice. If you roll a 6, you will win $300. If you roll a5, you will win $120. If you roll a 3 or 4, you will win $60. However, if you roll a 1 or 2, youwill not win anything. Let X be a random variable representing the amount that you will win.(a) What is the expectation of X?(b) What is the variance of X?(c) If you have won some money in the lucky draw, what is the probability that you havewon at least $120?

Given information, A lucky draw involves rolling six-sided dice. The probability of getting any…

Answered: A lucky draw involves rolling a…

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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Neighborhood Insurance sells fire insurance policies to local homeowners. The premium is $150, the probability of a fire is 0.1%, and in the event of a fire, the insured damages (the payout on the policy) will be $140,000. g. What are the expected value and variance of your profit?
You roll five fair six-sided dice. Let X denote the sum of the numbers shown. Compute the expectation and the variance of X.
Just answer as many problem you desire
You are playing a game at a carnival. It costs nothing to play. You can win $5 with probability 0.15 on each round, but if you lose, you pay $2. (a) Let X be the number of times it takes for you to get your first win. What distribution does X follow, and what are the expection and variance of X? (b) If you play until you win once, what is your expected net profit (positive for profit, negative for loss)? What is the variance? (c) You start with $20. What is the probability that you lose all of your money without winning even once?
An automotive center keeps track of customer complaints received each week. The probability distributions of complaints are shown below. The random variable, xi, represents the number of complaints, and p(xi) is the probability of receiving xi complaints for two of the stores. The cost impact of each complaint is believed to be y=$10x3 where x is the number of complaints. Store A xi 0 1 2 3 4 5 6 p(xi) 0.10 0.15 0.20 0.25 0.15 0.10 0.05 Store B xi 0 1 2 3 4 5 6 p(xi) 0.10 0.15 0.25 0.22 0.13 0.08 0.07 Compute the simulated averages and standard deviations of the number of complaints per week for each store and the total for both stores over the 52 weeks. Compare to the theoretical mean and standard deviations.
Q: If 5% of the people are carriers of a certain disease and 10% of them are young, what is the probability that the young person will be a carrier? For disease if we know that young people make up 20% of the population?
5
If the events A and B two disjoint even then P(AnB) =0.2 P(AnB) =0.6 II P(AnB) =0.8 .IV P(AnB) =1 %3D
The events of A and B are mutually exclusive. Suppose P(A) 0.2 and P(B) = 0.1. What is the probability of either A or B occurring? What is the probability that neither A nor B will happen? Next page TOSHIE
Your friend Phil, asks you what you think about a new scratch-off lottery game. It costs $10 to play this game, There are two outcomes for the game (win, lose) and the probability that a player wins a game is 60%. A win results in $15, for a net win of $5 ($15 minus the $10 paid to play). The probability distribution for x� (the amount of money a player wins or loses) in a single game is as follows:
Oscar is playing a simple card game. The game is played by the player picking a card from a deck. If the player picks any face cards, they wins $20. If the player picks any other cards, they lose $10. Let X be the random variable representing the $ amount Oscar will win/ lose from this game. (a) Fill in the probability distribution of X. Leave the probability as a fraction. X P(X) Win $ Lose $ (b) Calculate the expected value of X. Round your answer to the nearest hundredth of a dollar. (for example if the answer is 43.5478, then round to 43.55). The expected value is $
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