n how many ways can the two marbles be drawn from the bag so that at least one of the marbles is red?

[eddy2017]

Hi, there dear friends:

A bag contains four marbles. One marble is blue, one is red, one is white, and one is yellow. Two marbles are draw from the bag by removing one marble and then, without replacing the first marble, removing a second marble. In how many ways can the two marbles be drawn from the bag so that at least one of the marbles is red?

There are two marbles drawn. The problem is asking about combinations ("how many ways"), not about probability.

Solution
With one blue, one red, one white, one yellow marbles in the bag -- and without replacement (which is important) --
The possible results are:
B R
B W
B Y
R B (note: this "way" is different from B R)
R W
R Y
W B
W R
W Y
Y B
Y R
Y W

I do all possible combinations.
There are 6 possible combinations.
In how many ways do I have the possibility of drawing a red marble?. Well, in 6 different ways.

Is this good or am I missing something here?
Thanks a lot for your help and time.

 

[Romsek]

You need to be careful about whether order matters. The problem implies that it does as it says you pick one marble and then a second,
as opposed to saying you pick two marbles.

If order matters then there are 3 ways to pick 2 marbles with red as the first, and 3 ways to pick 2 marbles with red as the second, i.e. 6 ways.

If order does not matter, then there are just 3 ways to pick 2 marbles such that one is red.

Given that I think order matters in this problem I'd say the answer is 6 ways.

 

[JeffM]

The question as shown is very badly worded. For example, with only one red marble, what is the point of saying "at least one." As romsek says, the language does not make entirely clear whether it considers red and blue one way regardless of the order in which they were drawn, a focus on result, or whether it considers red first, then blue one way and blue first, then red a different way, a focus on process.

Did you give the exact and complete wording of the problem as it was given to you?

 

[eddy2017]

That is the exact wording. I posted something and then deleted it, because I realized what Romsek means by
'if order matters then there are 3 ways to pick 2 marbles with red as the first, and 3 ways to pick 2 marbles with red as the second, i.e. 6 ways.'
I think I understand now.
These are the three possible ways to pick two marbles with red first:
RB (note: this "way" is different from B R)


RW


RY

And the other three ways to pick 2 red-colored marbles as a second:
BR
WR
YR