S2 Binomial question NEED HELP

8

I have just started S2 and i am little stuck on this question, which appears to be simple but i am not to sure on my answer. The situation is:

A bag contains 4 red and 6 blue marbles. A marble is chosen at random, its colour is noted and it is then replaced in the bag. This procedure happens 11 times. Thanks in advance.

Sorry for not posting the question. It is in 2 parts.

What is the expected number of red marbles?

and

what is the most likely number of blue marbles drawn?

Reply 1

silent ninja

19

What is the question? You haven't posted it :hmmm:

Since the marbles are replaced, the probability of a particular coloured marble is constant. Write down the probability of each and then tackle the question. Depending on the question, you might notice what kind of distribution it follows.

Reply 2

trayder

OP

8

anyone there to help?

Reply 3

Koudoo

Okay I will set you off, as I have been told I give away answers too easy...

E(x) = np...

I suppose you can change the distirbution then work out each of the parts...

so you will use E(x) twice but with different np's...

PS if your still stuck or dont understand I will work out the answer for ya, do you have the answers btw so you can check yourself?

Reply 4

trayder

OP

8

For the first question i got 4. But for the second because they said likely i put 7. As if they are 11 trials they has to be either 5 red drawn and 6 blue or 5 red drawn and 7 blue. so i assumed as the probability to draw blue is higher than red, it what more likely for there to be 7 blue drawn and 4 red. Am i right in thinking this?

Reply 5

Koudoo

"A bag contains 4 red and 6 blue marbles. A marble is chosen at random, its colour is noted and it is then replaced in the bag. This procedure happens 11 times."

"What is the expected number of red marbles?"
X~B(11, 0.4)
E(x) = np
E(x) = 11 x 0.4 = 4.4

"What is the most likely number of blue marbles drawn?"
Y~B(11, 0.6)
E(x) = np
E(x) = 11 x 0.6 = 6.6

Usually E(x) (Expected values of X) are left with decimals, and not rounded to the nearest marble.

Reply 6

Koudoo

Do you have the answers?

Your thought process was right, but I don't think it would achieve you the full marks, since there is a direct method to solving the question.

Reply 7

trayder

OP

8

Koudoo

"A bag contains 4 red and 6 blue marbles. A marble is chosen at random, its colour is noted and it is then replaced in the bag. This procedure happens 11 times."

"What is the expected number of red marbles?"
X~B(11, 0.4)
E(x) = np
E(x) = 11 x 0.4 = 4.4

"What is the most likely number of blue marbles drawn?"
Y~B(11, 0.6)
E(x) = np
E(x) = 11 x 0.6 = 6.6

Usually E(x) (Expected values of X) are left with decimals, and not rounded to the nearest marble.

Thanks. That is what i initially did, but then i thought in real terms that you couldnt remove 6.6 marbles or 4.4. I was forgetting that this is statistics and it is theoretical.

Reply 8

trayder

OP

8

Koudoo

Do you have the answers?

Your thought process was right, but I don't think it would achieve you the full marks, since there is a direct method to solving the question.

Well it is multiple choice, but i dont have the answer sheet. The options for the first question are:

4, 4.4, 5 and 6.6

for th 2nd they are:

7, 6, 6.6 and 4.

Reply 9

Koudoo

Do they want the statistical answer or the nearest marble answer?

As thats the hardest thing about these questions, as I am never sure when you are expected to relate it back to the question and give a real answer, or leave it as a statistical answer :s-smilie:

...

Reply 10

trayder

OP

8

Koudoo

Do they want the statistical answer or the nearest marble answer?

As thats the hardest thing about these questions, as I am never sure when you are expected to relate it back to the question and give a real answer, or leave it as a statistical answer :s-smilie:

...

Yh that was the problem i encountered. But if we go back to the theory, the expected value is not always a possible outcome. So following the rules of statistics i think that your working out is correct. Because they havent said whether i should relate it to the real world.

Reply 11

Koudoo

At all the answer schemes I seen a long while back when I done it, they usually want the decimal/orginal answer, but you can get the odd question.

But I think the big trigger word is where they said "Expected value", and that also some of the choice options had decimals in...

I take it this isnt a exam question?

Reply 12

trayder

OP

8

No its just some sheet my teacher gave me. But with the second question it is worded differently i wonder if that one would be where you round it up to 7.

Reply 13

Koudoo

It might be, actually now that I think about it, it is since, the word "likely" means you answer will have to be a real possibility.

Reply 14

NOEMI0308

2

the second one is 7

S2 Binomial question NEED HELP

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