Tutorial 2 Questions

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School

University of Toronto *

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Course

236

Subject

Mechanical Engineering

Date

Jan 9, 2024

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Uploaded by CountClover9044

University of Toronto Department of Mechanical and Industrial Engineering MIE236: Probability (Fall 2023) Tutorial 2 Problem 1: Four married couples have bought 8 seats in the same row for a concert. In how many ways can they be seated a) with no restrictions? b) if each couple is to sit together? c) if all the men sit together to the right of all the women? Problem 2: How many ways are there that no two students will have the same birth date in a class of size 60? Problem 3: Suppose that in a senior college class of 500 students it is found that 210 smoke, 258 drink alcoholic beverages, 216 eat between meals, 122 smoke and drink alcoholic beverages, 83 eat between meals and drink alcoholic beverages, 97 smoke and eat between meals, and 52 engage in all three of these bad health practices. If a member of this senior class is selected at random, find the probability that the student a) smokes but does not drink alcoholic beverages; b) eats between meals and drinks alcoholic beverages but does not smoke; c) neither smokes nor eats between meals. Problem 4. If 3 books are picked at random from a shelf containing 5 novels, 3 books of poems, and a dictionary, what is the probability that a) the dictionary is selected? b) 2 novels and 1 book of poems are selected? Problem 5. Factory workers are constantly encouraged to practice zero tolerance when it comes to accidents in factories. Accidents can occur because the working environment or conditions themselves are unsafe. On the other hand, accidents can occur due to carelessness or so-called human error. In addition, the worker’s shift , 7:00 A.M. – 3:00 P.M. (day shift), 3:00 P.M. – 11:00 P.M. (evening shift), or 11:00 P.M. – 7:00 A.M. (graveyard shift), may be a factor. During the last year, 300 accidents have occurred. The percentages of the accidents for the condition combinations are as follows:

University of Toronto Department of Mechanical and Industrial Engineering MIE236: Probability (Fall 2023) Shift Unsafe Conditions Human Error Day 5% 32% Evening 6% 25% Graveyard 2% 30% If an accident report is selected randomly from the 300 reports, a) what is the probability that the accident occurred on the graveyard shift? b) what is the probability that the accident occurred due to human error? c) what is the probability that the accident occurred due to unsafe conditions? d) what is the probability that the accident occurred on either the evening or the graveyard shift? Problem 6: Fred is planning to go out to dinner each night of a certain week, Monday through Friday, with each dinner being at one of his favorite ten restaurants. 1. How many possibilities are there for Fred’s schedule of dinners for that week, if Fred is not willing to eat at the same restaurant more than once? 2. How many possibilities are there for Fred’s schedule of dinners for that week, if Fred is willing to eat at the same restaurant more than once, but not twice in a row (or more)? Problem 7: A round-robin tournament is being held with n tennis players; this means that every player will play against every other player exactly once. a) How many games are played in total? b) How many possible outcomes are there for the tournament (the outcomes list who won and who lost for each game).

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