Why Does the Order of Drawing Marbles Affect the Probability Calculation?

[DotKite]

Homework Statement

Consider a jar with 3 black marbles and 1 red, for the experiment of drawing two with replacement. What is the probability of drawing a black then a red in that order? Assume all marbles are equally likely to be drawn.

Homework Equations

The Attempt at a Solution

Ok first why do they say "find the probability in that order"? Why does order matter if you are taking two at a time? Then they say assume all marbles are equally likely to be drawn? Uhhhh what?

 

[Ray Vickson]

Homework Statement

Consider a jar with 3 black marbles and 1 red, for the experiment of drawing two with replacement. What is the probability of drawing a black then a red in that order? Assume all marbles are equally likely to be drawn.

Homework Equations

The Attempt at a Solution

Ok first why do they say "find the probability in that order"? Why does order matter if you are taking two at a time? Then they say assume all marbles are equally likely to be drawn? Uhhhh what?

It matters because that is what they have asked you to do. In some problems the order does not matter, but in this one it does. The problem never said you draw two at the same time; it just said you draw two.

 

[haruspex]

It matters because that is what they have asked you to do. In some problems the order does not matter, but in this one it does. The problem never said you draw two at the same time; it just said you draw two.

Moreover, if it were drawing two at the same time then it would not be 'with replacement'.

 

[DotKite]

It matters because that is what they have asked you to do. In some problems the order does not matter, but in this one it does. The problem never said you draw two at the same time; it just said you draw two.

Oh you are right! Fml

 

[DotKite]

Ok the problem is totally easy when you don't read it wrong lol.

So first draw of black is 3/4. Then you replace and the second draw of red is 1/4. So the prob of black then red is 3/16

 

[DotKite]

Ok there is a similar question

An urn contains four balls: one red, one green, one yellow, and one white.
Two balls are drawn without replacement from the urn. What is the probability of getting a red ball and a white ball. Ok so for red on the first draw is 1/4. Then for white on second draw we have 1/3. So the probability of red and white is 1/12 right?

Seems right to me but apparently the answer is .167?

 

[haruspex]

Ok there is a similar question

An urn contains four balls: one red, one green, one yellow, and one white.
Two balls are drawn without replacement from the urn. What is the probability of getting a red ball and a white ball.


Ok so for red on the first draw is 1/4. Then for white on second draw we have 1/3. So the probability of red and white is 1/12 right?

Seems right to me but apparently the answer is .167?

It says "a red ball and a white ball", not "a red ball then a white ball".