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Question 1 4/5 pts Three times each day a quality control engineer samples a component from a recently manufactured batch and tests it. Each part is given one of three classifications conforming - suitable for its intended use downgraded - unsuitable for its intended purpose, but usable for another purpose S scrap not usable An experiment consists of recording (in order) the classifications of the three parts tested on a particular day. List all of the outcomes in the sample space. (For example, two possible outcomes are CCS and DSC. CCS means that the first two parts were conforming, and the third was scrap. DSC means that the first was downgraded, the second was scrap, and the third was conforming. Note that this is not the same as CSD.) How many are there?Select ] Let A be the event that all the parts fall into the same category. How many outcomes are in event A? 3 Let B be the event that at least two parts are conforming. How many outcomes are in event B? Select] How many outcomes are in the event AnB? Select ] H t AnB?[Select] ow many outcomes are in the evern

Answer 1

Solution:

List all of the outcomes in the sample space. How many are there?

Answer: There are $\boldsymbol{3^3=27}$ possible outcomes and these are given below:

$\Omega =\begin{Bmatrix} CCC &CCD &CCS \\ CDC &CDD &CDS \\ CSC& CSD &CSS \\ DCC & DCD &DCS \\ DDC&DDD &DDS \\ DSC& DSD &DSS \\ SCC& SCD &SCS \\ SDC& SDD &SDS \\ SSC& SSD &SSS \end{Bmatrix}$

Let A be the event that all the parts fall into the same category. How many outcomes are in event A?

Answer: $\boldsymbol{3(CCC,DDD,SSS)}$

Let B be the event that at least two parts are conforming, How many outcomes in event B?

Answer: $\boldsymbol{7(CCC,CCD,CCS,CDC,CSC,DCC,SCC)}$

How many outcomes are in the event $A\cap B$ ?

Answer: $\boldsymbol{1(CCC)}$

How many outcomes are in the event $A\cap B'$?

Answer: $\boldsymbol{2(DDD,SSS)}$