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1. Given that P(A) =.P(B) = and P(AOB) = find P(AUB)

1. Given that P(A) =.P(B) = and P(AOB) = find P(AUB)

A First Course in Probability (10th Edition)
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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Probability Assessment 1 1. Given that P(Ã) =,P(B) = , and P(An B)= find P(AU B) 2. The pupils in a class were asked how many brothers and sister they had. Their answers are shown in the table: No. brothers & sisters 01 2 34 5 No. pupils 5 10 9 3 2 I If a child is chosen at random find the probability that there are 3 children in their family. 3. Two dice are thrown simultaneously and their scores are multiplied. P(n) denotes that probability that score n is obtained a) draw a possibility space diagram to represent the data Calculate: b) P(10) c) P(25) d) P(27) e) Given that P(t) =, find the possible values of t. 4. Events A and B are such that a) Find P(B|A) b) Find P(BnA) c) Are events A and B exhaustive? 5. I travel to work via route D or route E. The probability that I choose route D is 0.3 and the probability that I am late for work if I choose route D is 0.7, the corresponding probability if I go via route E is 0.2 a) What is the probability that I will be late for work tomorrow? b) Given that I am late for work, what is the probability that I go via route E? 6. Three people Ali, Brian and Charlie arrange to meet in a bar on campus. Ali cannot remember whether they agreed to meet in Origins or Mungo's and flips a coin to decide. Brian also flips a coin to decide between Mungo's and K-bar. Charlie flips a coin to decide whether to go to K-bar or not, in the latter case he flips again to decide between Origins and Mungo's. a) Draw one probability tree diagram to represent all the information. Find the probability that: b) Ali and Brian meet c) Brian and Charlie meet d) All 3 meet e) All 3 go to different places f) At least 2 of them meet.
Transcribed Image Text:Probability Assessment 1 1. Given that P(Ã) =,P(B) = , and P(An B)= find P(AU B) 2. The pupils in a class were asked how many brothers and sister they had. Their answers are shown in the table: No. brothers & sisters 01 2 34 5 No. pupils 5 10 9 3 2 I If a child is chosen at random find the probability that there are 3 children in their family. 3. Two dice are thrown simultaneously and their scores are multiplied. P(n) denotes that probability that score n is obtained a) draw a possibility space diagram to represent the data Calculate: b) P(10) c) P(25) d) P(27) e) Given that P(t) =, find the possible values of t. 4. Events A and B are such that a) Find P(B|A) b) Find P(BnA) c) Are events A and B exhaustive? 5. I travel to work via route D or route E. The probability that I choose route D is 0.3 and the probability that I am late for work if I choose route D is 0.7, the corresponding probability if I go via route E is 0.2 a) What is the probability that I will be late for work tomorrow? b) Given that I am late for work, what is the probability that I go via route E? 6. Three people Ali, Brian and Charlie arrange to meet in a bar on campus. Ali cannot remember whether they agreed to meet in Origins or Mungo's and flips a coin to decide. Brian also flips a coin to decide between Mungo's and K-bar. Charlie flips a coin to decide whether to go to K-bar or not, in the latter case he flips again to decide between Origins and Mungo's. a) Draw one probability tree diagram to represent all the information. Find the probability that: b) Ali and Brian meet c) Brian and Charlie meet d) All 3 meet e) All 3 go to different places f) At least 2 of them meet.
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