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.

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.)