Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Box of Toy Cards

Jack has a box of toys cars. There are 5 red cars and 6 blue cars. Jack randomly selected 2 cars from the box with replacement. What is the probability that he will draw one red car and 1 blue cars?

Let me see.

Let A = selecting a red car.

Let B = selecting a blue car.

This is a dependent event because it is with replacement.

P(A) = 5/11

Since the red car was placed back into the box it does not effect the probability of selecting a blue car.

P(B) = 6/11

I want P(A and B) = P(A) • P(B).

P(A and B) = 5/11 • 6/11

P(A and B) = 30/121

Is this right?

Last edited by mathxyz (2024-05-12 02:36:42)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Box of Toy Cards

one red car and 2 blue cars?

Looks like you meant one of each.

Your answer is good if you want the red first then blue second.  I suspect not in which case you need to do like in a previous post and work out the blue then red probability and add the two answers.  (it'll be one answer times 2)

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: Box of Toy Cards

one red car and 2 blue cars?

Looks like you meant one of each.

Your answer is good if you want the red first then blue second.  I suspect not in which case you need to do like in a previous post and work out the blue then red probability and add the two answers.  (it'll be one answer times 2)

Bob

Yes, I meant one of each type of car. I will edit my post now. This is problem is in terms of replacement not without replacement. In that case, am I right in my work? I will post a few more of with replacement and without replacement samples throughout the day. This will be my only topic today.

Last edited by mathxyz (2024-05-12 01:18:11)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Box of Toy Cards

The answer was correct for red then blue.

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: Box of Toy Cards

The answer was correct for red then blue.

Bob

Very good. I will post a few more of this type of probability problem throughout the day.

Let me see if I get it.

With replacement means the item is placed back in the box, in the bag, etc

Without replacement means the item is not placed back in the box, in the bag, etc.

Is this right?

Last edited by mathxyz (2024-05-12 06:03:13)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Box of Toy Cards

You meant "Without replacement means the item is not placed back in the box, in the bag

B

---

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: Box of Toy Cards

You meant "Without replacement means the item is not placed back in the box, in the bag

B

Yes, correct. I edited my typo.