Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Bag of Marbles

A bag contains 20 marbles. There are 5 red, 5 blue, 5 green, 5 yellow.
Two marbles are drawn without replacement. What is the probability of drawing 2 blue marbles?

Let me see.

Without replacement means marble was not placed back into the bag.
I think this is known as Dependent Event. P(A) • P(B|A).

The P(A) • P(B) GIVEN THAT P(A) has occurred.

Let A = selecting a blue marble.

Let B = selecting a blue marble.

P(A) = 5/20 = 1/4.

P(B) = 4/19.

P(A and B) = (1/4)(4/19) = 1/19.

Is this right?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Bag of Marbles

Yes.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Bag of Marbles

Yes.

Bob

This will be my topic today. I can do this in terms of college algebra and possibly precalculus material. In terms of calculus, I have to go through the entire textbook by the late James Stewart if I really want to grasp the material. If I go through the entire college algebra textbook and the entire precalculus textbook, I will never get to calculus which is my ultimate goal in this self-study of mathematics.

I go back to work Wednesday night after more than 7 weeks unemployed. When I return to my overnight hours, I will only be able to learn and review one topic at a time. A sad reality for me at 59 since retirement is no where in sight.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Bag of Marbles

Do you have to work through in order. What happens if you skip straight to calculus.  You'll find some gaps that mean you have to backtrack but I think you'll get to your goal more quickly.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Bag of Marbles

Do you have to work through in order. What happens if you skip straight to calculus.  You'll find some gaps that mean you have to backtrack but I think you'll get to your goal more quickly.

Bob

You make sense every time.

Let's do this:

1. I will randomly select questions from my college algebra and precalculus textbooks to review. I took and passed college algebra and precalculus back in the 1990s. This is just a review of material learned decades ago.

2. At the same time, I can start with Calculus 1 for which I will need to study chapter by chapter and section by section.

3. There is no rush for any of this, right? It's not like I have to prepare for a test or my next classroom. I can also watch professor Leonard on YouTube. He downloaded Calculus l, ll, and lll as he taught each course in the classroom.

4. A major problem for me with Calculus is learning Latex. It is impossible to type certain problems without using Latex. 

5. There are also tons of problems requiring geometric figures which means uploading pictures here which I have not been able to do with my android phone. I don't have a computer or laptop and don't know when I will be able to buy one in the uncertainty of my job situation.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Bag of Marbles

Let's try.  Here's some calculus related Latex.  If you click on it the forum should show you the underlying commands so you can copy them as needed.  Don't forget the math /math at the start and end inside  [        ].

Notes about the second example

(1) Latex doesn't recognise spaces so the word Evaluate and the integral symbol get squished together. To stop this I have inserted an extra \ which has the effect of leaving a space.

(2) The biggest headache I have with Latex is getting the {} brackets correct. If you leave one out then the interpreter cannot do its job.

The \frac command needs four: {numerator}{denominator}  For the \int command I have put the whole expression inside {} as well.

(3) The large round brackets are because of the \left and \right commands. You must always have both. The interpreter will get confused if you have a large open bracket but forget the large close bracket command.  I think it allows [ ] type brackets so if your expression is very complicated with multiple brackets you can switch type as long as the close type matches the open type. ie don't do this (]

(4) if you want integral limits then after the word int no spaces but rather underscore and the limit; then ^ and the top limit.  That's all if the numbers are a single digit. If you want something bigger for the limit enclose it in {}. here's an example.

eg

The lower limit after the underscore is in {} brackets. It is a frac command so it has {}{} .  The upper limit is more than a single character so it is also in {}. Finally the actual expression to be integrated is in {}.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Bag of Marbles

Let's try.  Here's some calculus related Latex.  If you click on it the forum should show you the underlying commands so you can copy them as needed.  Don't forget the math /math at the start and end inside  [        ].

Notes about the second example

(1) Latex doesn't recognise spaces so the word Evaluate and the integral symbol get squished together. To stop this I have inserted an extra \ which has the effect of leaving a space.

(2) The biggest headache I have with Latex is getting the {} brackets correct. If you leave one out then the interpreter cannot do its job.

The \frac command needs four: {numerator}{denominator}  For the \int command I have put the whole expression inside {} as well.

(3) The large round brackets are because of the \left and \right commands. You must always have both. The interpreter will get confused if you have a large open bracket but forget the large close bracket command.  I think it allows [ ] type brackets so if your expression is very complicated with multiple brackets you can switch type as long as the close type matches the open type. ie don't do this (]

(4) if you want integral limits then after the word int no spaces but rather underscore and the limit; then ^ and the top limit.  That's all if the numbers are a single digit. If you want something bigger for the limit enclose it in {}. here's an example.

eg

The lower limit after the underscore is in {} brackets. It is a frac command so it has {}{} .  The upper limit is more than a single character so it is also in {}. Finally the actual expression to be integrated is in {}.

Bob

I will start Calculus 1 as soon as I get my new days off from the boss at the new job which hopefully begins on May 15. My work schedule has not been confirmed. I also need time to learn the basics of Latex.

NOTE: IF MY ANDROID PHONE GIVES ME A HARD TIME WITH LATEX, I WILL USE ABBREVIATIONS AND EXTRA VARIABLES TO REPRESENT WHAT I AM TRYING TO DO.