Question

QUESTION 19 A standard slot machine like this one (link) has three wheels that turn independently with various symbols on them. Almost all slot machines now are controlled by computers that generate random numbers corresponding to certain winning and losing combinations of symbols. In the early days of slot machines, pulling the lever or "arm" to start spinning the wheels actually allowed the gambler to interact with the mechanics of the machine (thereby opening the door to all kinds of odd good-luck rituals). Now, slot machine outcomes "play by wire," in that pulling the lever does not actually making anything move, but rather just sends a signal to the computer to generate a random number corresponding to a particular outcome. Now, to the actual problem. Suppose each wheel in a slot machine has 10 symbols that are equally likely to come up: four "BAR" symbols; three lemons, two cherries, and one bell. You decide to play one time. What is the probability that all three lemons will appear, to three decimal places? Hint: What is P(Lemon) on any one wheel? Also, don't forget to assume that each wheel turns independently of the others.

QUESTION 8 A quality control inspector receives a box of 3 items. Unknown to him, 1 of the items is defective. He draws two items from the box, one after the other, without replacing the first part drawn before drawing the second part. What is the sample space in terms of defective (D) and acceptable (A) parts? Hint: Distinguish between two parts that are acceptable or two parts that are defective by using subscripts. For example, two acceptable parts could be identified as A1 and A2.

S = {DA1, DA2}

S = {DA1, DA2, A1A2}

S = {DA1, DA2, A1A2, A2D}

S = {D1A1, D2A2, A1A2, D1D2}

S = {D,DA,DAA,DAAA,DAAA,...}

QUESTION 5 Suppose that the experiment is asking 5 students at SHSU what their classification is (either freshman, sophomore, junior, senior, or graduate), one after the other. How many outcomes would be in the sample space S?

Answer 1

Question 19) There are 10 symbols in each wheel, out of which 3 are lemons. Thus the probability of getting a lemon when we rotate the wheel is 3/10.

that is, P(lemon) on any one wheel = 3/10

There are three wheels in a slot machine. Since each wheel turns independently of others, all the three wheels have this same probability of getting a lemon. (When two events are said to be independent of each other, what this means is that the probability of one event occurs in no way affects the probability of other event occurring)

When it comes to independent events, the probability of events a,b & c will be the product of probabilities of a,b & c

That is, P(A∩B∩C) = P(A)P(B)P(C)

So, the probability of getting a lemon on all three wheels = (3/10) * (3/10) * (3/10)

(it can be written as (3/10) ³ also)

Probability of getting a lemon on all three wheels = 3³ / 10³ = 27/1000= 0.027

Question 8) There are 3 parts in the box. 2 acceptable parts (A1 & A2) and one defective part (D)

Since the parts are taken without replacing, it can't be repeated in a single element of sample space. (that is, we can't include A1A1, or A2A2)

Thus the sample space, S = { DA1, DA2, A1A2 }

Question 5)

There are 5 students and each student can be any of the 5 classifications (either freshman, sophomore, junior, senior, or graduate). So total elements in the sample space would be 5⁵= 3125

explanation:

Let's denote the classifications by freshman=f, sophomore=s, junior=j, senior=e, graduste=g and the five students be 1,2,3,4 and 5.

And 1f means student 1 is a freshman and 3g means student 3 is a graduate and so on..

Then the sample space would look something like this,

S= { (1f,2f,3f,4f,5f), (1f,2f,3f,4f,5s), (1f,2f,3f,4f,5j),.................(1f,2f,3f,4s,5f)..........(1j,2j,3e,4f,5g)...............(1g,2g,3g,4g,5g)}

That is, every student can have any 5 classifications.

Student 1, can be either f,s,j,e,g. =5, Student 2, can be either f,s,j,e,g. =5, etc

Since this is true for every student, the number of combinations would be 5x5x5x5x5 = 5⁵

(Remember this is equal to the number of classifications ^{number of students} and not vice versa. that is,if instead of 5, we asked the same question to 3 students, the answer would be 5³ and not 3⁵)