Probability of Removing and not Removing

[zak100]

Homework Statement

A jar has 5 marbles, 1 of each of the colors red, white, blue, green and yellow. If 4 marbles are removed from the jar, what is the probability (i) that the yellow one was removed? (i) that the yellow one was not removed?

Homework Equations

probability = favorable outcomes/total outcomes

The Attempt at a Solution

i) 4/5
ii) 4/5

One answer not correct. Some body please guide me.

Zulfi.

 

[DrClaude]

You'll have to give more details about how you arrived at those solutions.

 

[Ray Vickson]

Homework Statement

A jar has 5 marbles, 1 of each of the colors red, white, blue, green and yellow. If 4 marbles are removed from the jar, what is the probability (i) that the yellow one was removed? (i) that the yellow one was not removed?

Homework Equations

probability = favorable outcomes/total outcomes

The Attempt at a Solution

i) 4/5
ii) 4/5

One answer not correct. Some body please guide me.

Zulfi.

Which answer is correct?

 

[zak100]

Hi,
Thanks for your response.

probability = favorable outcomes/total outcomes

I think the total outcomes is 4 because at a time we are picking 4 marbles.Now the probability that it is removed is 1/4, because out of 4 only 1 would be the yellow.
And the probability that it is not removed is: 4/4 because it is possible that out of 4 none of them is yellow.

Answer is not correct so please guide me.

Zulfi.

 

[Ray Vickson]

Hi,
Thanks for your response.

probability = favorable outcomes/total outcomes

I think the total outcomes is 4 because at a time we are picking 4 marbles.Now the probability that it is removed is 1/4, because out of 4 only 1 would be the yellow.
And the probability that it is not removed is: 4/4 because it is possible that out of 4 none of them is yellow.

Answer is not correct so please guide me.

Zulfi.

What you wrote above is WRONG. If you had a removal event with probability 1/4, the probability of the non-removal event would have to be 3/4 (because two events {removal} and {non-removal} are mutually exclusive and "exhaustive"---- meaning that together they give all the possibilities and so have probabilities that sum to 1).

Anyway, the 1/4 is also wrong.

You need to think more carefully about what you are doing. You should always approach such problems systematically, until you are a lot more experienced. So, the steps you should always follow are:
(1) describe the "sample space" of the experiment---which is the set of all possible outcomes;
(2) assign probabilities to the individual outcomes in the sample space;
(3) obtain the probability of an event of interest by adding together all the individual-outcome probabilities for those outcomes that belong to your event.

For example, when you draw 4 items from 5 differently-colored items you can have a sample-space consisting of all 4-letter strings of the form ABCD, where A is one of the five colors (R,W,G,B,Y), B is another one of the five colors, etc. You may then be interested in the event NY = {no Y} = {no yellow}; this consists of all the 4-letter strings having no letter Y. So, if you assume that all the 4-letter strings are equally likely then you can say that
$$P\{ \text{no yellow}\} = \frac{\text{ number strings not containing Y}}{\text{total number of strings}}\; \hspace{2mm} (1)$$

Have you computed the numerator and denominator of the fraction in (1)?

 

[haruspex]

I think the total outcomes is 4 because at a time we are picking 4 marbles.

If you were only picking one marble, would there be only one possible outcome?

 

[zak100]

Hi,
Thanks. God bless you. I am able to understand the concept.

If you were only picking one marble, would there be only one possible outcome?

No. There would be five possible outcomes. It means i can get any of the 5 marbles. So there are altogether 5 total outcomes.

i)that the yellow one was removed?

Probability of removing yellow would be 1/5 because there is only one yellow marble.

(i) that the yellow one was not removed?

Probability of not removing yellow would be 4/5 because there are 4 non- yellow marbles.

Zulfi.

 

[haruspex]

Hi,
Thanks. God bless you. I am able to understand the concept.
No. There would be five possible outcomes. It means i can get any of the 5 marbles. So there are altogether 5 total outcomes.

i)that the yellow one was removed?

Probability of removing yellow would be 1/5 because there is only one yellow marble.

(i) that the yellow one was not removed?

Probability of not removing yellow would be 4/5 because there are 4 non- yellow marbles.

Zulfi.

Yes.

 

[Ray Vickson]

Hi,
Thanks. God bless you. I am able to understand the concept.
No. There would be five possible outcomes. It means i can get any of the 5 marbles. So there are altogether 5 total outcomes.

i)that the yellow one was removed?

Probability of removing yellow would be 1/5 because there is only one yellow marble.

(i) that the yellow one was not removed?

Probability of not removing yellow would be 4/5 because there are 4 non- yellow marbles.

Zulfi.

Yes, that is the solution for drawing one marble.

Now you need to extend it to drawing four marbles (without replacement).

However, to get a grasp of the more complicated problem I suggest you go next to the case of drawing two marbles, and leave the 4-marble case for later. (Eventually you will need to deal with the 4-marble case, but you can "sneak up on" the final problem by dealing first with simpler versions.)