A player of a video game is confronted with a series of opponents and has 60% probability of defeating each one. Success with any opponent is independent of previous encounters. Until defeated, the player continues to contest opponents. a) What is the probability distribution function of the number of opponents contested in a game? b) What is the probability that a player defeats at most two opponents in a game? c) What is the expected number of opponents contested in a game? d) What is the probability that a player contests two or more opponents in a game?

A player of a video game is confronted with a series of opponents and has 60% probability of defeating each one. Success with any opponent is independent of previous encounters. Until defeated, the player continues to contest opponents. a) What is the probability distribution function of the number of opponents contested in a game? b) What is the probability that a player defeats at most two opponents in a game? c) What is the expected number of opponents contested in a game? d) What is the probability that a player contests two or more opponents in a game?

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...

See similar textbooks

Similar questions

at a certain school, 34% of the students will qualify for financial aid type A and 19% will qualify for financial aid type b. if it is known that 5.1% of the students will qualify for both types of financial aid find: find the probability that a student will qualify for financial aid (at least one of either type A or type B) the probability that a student will qualify for type a and not type b
An assembly consists of three mechanical components. Suppose the probabilities that the first, second, and third components meet the specifications are 0.95, 0.98, and 0.99, respectively. Assume that the components are independent. 1) What is the probability that all components in an assembly meet specifications? 2) Determine the probability function of the number of components in the assembly that meet the specifications? x ? ? ? ? pX=x ? ? ? ?
(TATTOOS MAY LOOK UGLY IN OLD AGE) Among 250 employees of a Tattoo Company, a total of 130 have tattoos. There are 150 males working for this company and 85 of the males have Tattoos while uwmit tattoos. Tattoo Artist v What is the probability that an employee selected at random: Is A. 0.78 a female? B. 0.6000 v What is the probability that an employee selected at random: c. 0.26 has a tattoo? D. 0.18 v What is the probability that an employee selected at random: Is a female and has a tattoo? v What is the probability that an employee selected at random: Is E. 0.4800 F. 0.40 a male and does not have tattoo? G. 0.66 v What is the probability that an employee selected at random: Is male or has a tattoo? v What is the probability that an employee selected at random: 1. 0.2200 Is a female or does not have a tattoo? v Assume we selected a female of the company, what is the conditional probability she has no tattoo? H. 0.52 I. 0.55 K. 0.5667 Assume we selected a male from the company, what…
Based on a survey, assume that 27% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when five consumers are randomly selected, exactly two of them are comfortable with delivery by drones. Identify the values of n, x, p, and q.
In a game of blackjack played with one deck, a player is initially dealt 2 different cards from the 52 different cards in the deck. A winning blackjack hand is won by getting 1 of the 4 aces, and 1 of 16 other cards worth ten points The two cards can be in any order. Find the probability of being dealt a blackjack hand. What approximate percentage of hands are winning blackjack hands?
Based on a survey, assume that 44% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when five consumers are randomly selected, exactly three of them are comfortable with delivery by drones. Identify the values of n, x, p, and q.
It has been observed that the average number of accidents that occur on an assembly line is 3 per week. Find the probability that: i. A particular week will be accident free. ii. At least three (3) accidents will occur in a week. iii. Exactly five (5) accidents will occur in two week
Based on a survey, assume that 33% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when sixconsumers are randomly selected, exactly two of them are comfortable with delivery by drones. Identify the values of n, x, p, and q.