# What is the probability of picking certain marbles?

#### DbsMom

##### New member
I am helping my daughter with math and we have this question:
There is a bag with three black marbles, 5 yellow marbles, 2 white marbles, 4 blue marble, and 1 green marble what is the probability of picking a white or black marble?
Any help is appreciated.

#### tkhunny

##### Moderator
Staff member
Roughly: Probability of Event = (# of desired events)/(Total # of events)

Counting White or Black: 2 + 3
Counting All: 3+5+2+4+1

On the other hand, it's a TERRIBLE question!! The probability of an event must, of necessity, presuppose that one actually makes the attempt. If you NEVER draw a marble from the bag, the probability of drawing White or Black is zero (0).

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#### Subhotosh Khan

##### Super Moderator
Staff member
How many marbles are white - in the given bunch?

How many marbles are there - in total?

What is the probability of picking one white marble out of "all" those marbles? ........................................(1)

Similarly:

What is the probability of picking one black marble out of "all" those marbles? ........................................(2)

#### DbsMom

##### New member
Roughly: Probability of Event = (# of desired events)/(Total # of events)

Counting White or Black: 2 + 3
Counting All: 3+5+2+4+1

On the other hand, it's a TERRIBLE question!! The probability of an event must, of necessity, presuppose that one actually makes the attempt. If you NEVER draw a marble from the bag, the probability of drawing White of Black is zero (0).
It is a terrible question. The teacher presents it one way and then throws something different at the kids for their homework.
1/3 1/5 5/10 4/15. I think of the answers presented 1/3 makes the most sense. Right? But that would be picking both, not either or? I am so confused.

#### DbsMom

##### New member
How many marbles are white - in the given bunch?

How many marbles are there - in total?

What is the probability of picking one white marble out of "all" those marbles? ........................................(1)

Similarly:

What is the probability of picking one black marble out of "all" those marbles? ........................................(2)

Thank you! So 1/5 is the answer if the available answers are 1/3, 1/5, 5/10 or 4/15.

#### tkhunny

##### Moderator
Staff member
It is a terrible question. The teacher presents it one way and then throws something different at the kids for their homework.
1/3 1/5 5/10 4/15. I think of the answers presented 1/3 makes the most sense. Right? But that would be picking both, not either or? I am so confused.
Simply showing exact examples for every conceivable problem is not a good idea. If mathematics were all about memorizing, that might be fine. Part of the teaching of mathematics is the hope that a student might stretch and find solutions to problems they may not have seen, exactly.

#### tkhunny

##### Moderator
Staff member
Thank you! So 1/5 is the answer if the available answers are 1/3, 1/5, 5/10 or 4/15.
How did you get 1/5?

Please note that "if the available answer are..." has very little to do with the correct solution to the problem. If the correct answer is not listed, the correct answer remains the correct answer.

#### DbsMom

##### New member
Thank you. I agree.

#### Dr.Peterson

##### Elite Member
It is a terrible question. The teacher presents it one way and then throws something different at the kids for their homework.
1/3 1/5 5/10 4/15. I think of the answers presented 1/3 makes the most sense. Right? But that would be picking both, not either or? I am so confused.
The problem with the question itself is that it is not worded very carefully. Something has to be said about how the choosing is done, like this: "one marble is chosen randomly", as opposed to "two marbles are chosen without replacement."

The answer is 1/3; but your comment suggests you may have a common misunderstanding of the words "and" and "or" in probability. "Picking a white OR black marble" is satisfied (that is, the event occurs) when you pick any of those 5 marbles (the SUM of the number of white and the number of black); you are only picking one, so you can't pick both a white AND a black marble.

The same is true when we talk about sets. The set A = (1, 2} consists of the elements 1 AND 2, but would be described as "x is in the set if it is 1 OR 2". That's because in talking about sets or events, we are thinking of the individual elements or outcomes separately ("this happens OR that happens"), not of the list as a whole ("the event consists of this AND that").

#### DbsMom

##### New member
Thank you for explaining this. Math was my worst subject in school. I am reaching the limit of how I can help my kid. I will pass your detailed explanation on to her.

#### tkhunny

##### Moderator
Staff member
That's the spirit!

#### DbsMom

##### New member
Thank you so much. You have been so helpful. Are you a math teacher or educator?

#### tkhunny

##### Moderator
Staff member
Thank you so much. You have been so helpful. Are you a math teacher or educator?
We have all kinds, here. Ph.D.'s, professors, a few hacks, various sorts of teachers, website owners/administrators, scientists, and maybe an actuary. The same person may fall into multiple categories. We're all glad to help.

#### Jomo

##### Elite Member
You forgot to mention Denis, or was he one of the hacks.

#### tkhunny

##### Moderator
Staff member
I was including myself as a hack, having never had an actual classroom with my name on it. Others who wish to join the designation may do so voluntarily.

#### mmm4444bot

##### Super Moderator
Staff member
… Others who wish to join the designation may do so voluntarily.
Count me in!

I gotta a bit of experience in a LOT of things, which means I'm accomplished in nothin'.