Probability Word Question - Sheep, Ewes, Mature: A farmer has 100 sheep in a field...

patelsm

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Hi all,

Can you please help me with this:

A farmer has 100 sheep in a field. 60% of the sheep are ewes and the rest are rams. 80% of the sheep are lambs and the rest are mature sheep.
75% of the sheep are white and the rest are black.
How many sheep in the field are likely to be black, mature rams.

The answer is 2.


Somebody suggested this, but I still do not get it:

[FONT=&quot]100 sheep[/FONT]
[FONT=&quot]25% are black ie 25[/FONT]
[FONT=&quot]20% are mature ie 1/5 of 25 = 5[/FONT]
[FONT=&quot]40% are rams 5 x 0.4 = 2

[/FONT]
Please help.

Saf
 
Hi all,

Can you please help me with this:

A farmer has 100 sheep in a field. 60% of the sheep are ewes and the rest are rams. 80% of the sheep are lambs and the rest are mature sheep.
75% of the sheep are white and the rest are black.
How many sheep in the field are likely to be black, mature rams.

The answer is 2.


Somebody suggested this, but I still do not get it:

100 sheep
25% are black ie 25
20% are mature ie 1/5 of 25 = 5
40% are rams 5 x 0.4 = 2

Please help.

Saf

I think you're expected to assume the traits are independent. (It's conceivable that color could be sex-linked, or that white lambs become black when they mature, but that's unlikely, and without such information, you couldn't answer the question.)

Do you see how that helps, and leads to the answer you were given?
 
Hi all,

Can you please help me with this:

A farmer has 100 sheep in a field. 60% of the sheep are ewes and the rest are rams. 80% of the sheep are lambs and the rest are mature sheep.
75% of the sheep are white and the rest are black.
How many sheep in the field are likely to be black, mature rams.

The answer is 2.


Somebody suggested this, but I still do not get it:

100 sheep
25% are black ie 25
20% are mature ie 1/5 of 25 = 5
40% are rams 5 x 0.4 = 2

Please help.

Saf

start with the question.
How many sheep in the field are likely to be black, mature, rams?

you know first you have 40 rams, (40% of 100).
then what is the "likely" percentage of the rams to be mature?
then what is the "likely" percentage of the mature rams to be black?

you are told right off there are 40 rams.
then you assume an "even distribution" of mature (and black) sheep.
 
I think you're expected to assume the traits are independent. (It's conceivable that color could be sex-linked, or that white lambs become black when they mature, but that's unlikely, and without such information, you couldn't answer the question.)

Do you see how that helps, and leads to the answer you were given?

Hi DrP,

By initially reading the question, I did not perceive the categories of these 100 sheep to split into them being Black Mature Ram, White Mature Ram, Black Lamb Ram, White Lamb Ram, Black Mature Ewes, White Mature Ewes etc.
The below approach and the one given by SINX (thanks very much mate) only makes sense if the question was worded a bit differently - for instance, 25% are black and then from the 25%, 20% are mature and from the 25% 40% are rams.
Am I right in saying this?


100 sheep

25% are black ie 25
20% are mature ie 1/5 of 25 = 5
40% are rams 5 x 0.4 = 2
 
Hi DrP,

By initially reading the question, I did not perceive the categories of these 100 sheep to split into them being Black Mature Ram, White Mature Ram, Black Lamb Ram, White Lamb Ram, Black Mature Ewes, White Mature Ewes etc.The below approach and the one given by SINX (thanks very much mate) only makes sense if the question was worded a bit differently - for instance, 25% are black and then from the 25%, 20% are mature and from the 25% 40% are rams.
Am I right in saying this?


100 sheep

25% are black ie 25
20% are mature ie 1/5 of 25 = 5
40% are rams 5 x 0.4 = 2

Correct. And that's what "independent" means, if you are learning something about probability. (I stated that briefly, just as a hint, expecting you to ask if you didn't know what I meant.)

It means that not only are 20% of all the sheep mature, but 20% of any particular category are mature, and so on. As I pointed out, this might not be true, which is why they talk only about what is "likely", and why I didn't really like the question. In effect, you are guessing (reasonably) that each percentage applies "across the board".

Putting it all together, 25% are black; 20% of the 25% are mature black sheep; 40% of 20% of 25% of 100 are black, mature rams: .40*.20*.25*100 = 2.
 
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