2S2122 Activity 1.1

Instructions

Answer the following problems individually and truthfully.
Be sure to show your solutions and please box your final answers.
Please write your complete name, student number, and section on the upper left corner of your answer sheet. No name, student number, and section, no grade.
Save your answers in pdf file type with the filename format "section_lastname_firstname_studentnumber.pdf" all in small caps. For example: "abc_wayne_bruce_201101474.pdf".
Submit your files in the respective submission bin in UVLE. Be sure to submit in the correct class!
Have fun doing these exercises :) even though it may seem boring.
You only have two weeks to work on the activities. We will post the hard deadline on UVLE.

Bonus: If you want to submit an elegant work, you may want to try Overleaf. It's a document processing site where you encode your work using Latek. It's about time you learn this because you will use this when you graduate.

Grading Rubrics

If you have a good solution and a correct answer, you get full points.
If you have a good solution but the answer is not boxed (or highlighted), you get a 5% deduction of the total points for that problem.
If you have a good solution but the answer is wrong, you get a 20% deduction of the total points for that problem.
If your solution is somewhat OK but incomplete. You only get 40% of the total problem.
If you have a bad solution but with a correct answer. That sounds suspicious. You get 0% for that problem. A bad solution may be:
- You just wrote the given.
- You just dumped equations but no explanation to where they are used.
- You attempted to put a messy flow to distract us. That's definitely bad.
No attempt at all means no points at all.

Problem 1 (2 pts)

Three fair coins are tossed successively.

(a) Write down the sample space. (0.1 pts)

(b) What are the events for when the first coin is a head? Let this be event $E$ . (0.15 pts)

(c) What are the events for when the second coin is a tail? Let this be event $F$ . (0.15 pts)

(d) Calculate $P(E\cup F)$ . (0.4 pts)

(e) Calculate $P(E\cap F)$ . (0.4 pts)

(f) Calculate $P({\bar {E}})$ . (0.4 pts)

(g) Calculate $P({\bar {F}})$ . (0.4 pts)

Problem 2 (2 pts.)

Two events $A$ and $B$ are such that $P(A)=0.45$ , $P(B)=0.22$ , and $P(A\cup B)=0.53$ . Find $P({\bar {A}}\cup {\bar {B}})$ . (2 pts)

Problem 3 (2 pts.)

In a factory producing IC chips, the total quantity of defective items found in a given week is $14\%$ . It is suspected that the majority of these come from two machines, $X$ and $Y$ . An inspection shows that $8\%$ of the output from $X$ and $4\%$ of the output from $Y$ is defective. Furthermore, $11\%$ of the overall output came from $X$ and $23\%$ from $Y$ . An IC chip is chosen at random and found out to be defective. What is the probability that it came from either $X$ or $Y$ ? (*Hint*: Read very carefully.) (2 pts.)