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I am stuck while solving below probability problem? Anyone in position to help me over here Question: Suppose a farmer has 40 cattle in his herd, of which 10 have ideal muscle structure and 4 have rare markings, with 1 cow having both traits. He brings 10 cattle to show which have ideal muscle structure or rare markings. Just 30% of the cattle brought to show have rare markings (3/10), but just one of the cattle with ideal muscle have rare markings (and 100% of the cattle without ideal muscle structure brought to show have rare markings). i. What is the probability that the cow brought to show has ideal muscle structure but no rare markings? ii. What is the probability that cow brought to show has rare markings but not ideal muscle structure? iii. What is the probability that the cow brought to show has rare markings and ideal muscle structure?

Pakard
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  • First you say *"He brings 10 cattle to show"*; but then the questions ask about *"the cow brought to show"*. I'm confused. Did the farmer bring 1 or 10 cattle to show? – Stef Nov 29 '21 at 10:57
  • Also, the questions ask about probabilities, but there was no mention of anything random in the description. Did the farmer use a random process to choose the cattle to bring to show? – Stef Nov 29 '21 at 10:58
  • This is one confusing problem statement. Do yourself a favor: draw a Venn diagram. – duffymo Nov 29 '21 at 15:19
  • Farmer brought 10 cattle to show. Its a random selection process. – Pakard Nov 29 '21 at 15:31
  • Got it. Randomly selected from the 40 in the starting population. There are also statements about the outcome of that "random" selection. – duffymo Nov 29 '21 at 16:56
  • I’m voting to close this question because you should ask it on [math.se], rather than on this site. – Peter O. Nov 29 '21 at 19:18

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There's some wording issue in your question that makes it confusing, but I will propose a solution based on my understanding. You are either posting the question wrongly or there are a lot of redundant information to make the question confusing.

Let's define the following categories (sets):
A: a cattle has an ideal muscle structure
B: a cattle has a rare markings
and let cattle in any of those sets be called special compared to other cattles.

We are given the cardinalities of those sets. That is
n(A) = 10, n(B) = 4, n(A intersect B) = 1 also we can get n(A union B) = 13.

Your sentence "He brings 10 cattle to show which have ideal muscle structure or rare markings" means, he is bringing 10 out of those 13 to the show (not 40). Also, you are not telling us how he is selecting those 10, so I will assume he is selecting those 10 special cattle at random (each have the same probability of being selected).

Now, we know that out of 10 selected cows 3 have rare marking, 7 have ideal muscle and 1 has both. So,

i. What is the probability that the cow brought to show has ideal muscle structure but no rare markings? - which cow?
A proper question would be "Among the cows brought to the show, if we select a cow at random, what is the probability that the cow has ideal muscle structure but no rare markings". In this case the answer is trivial. 7 have ideal muscle structure, 1 has both so 6 have only idea muscle so the probability will be 6/10.

Same for your other questions. Note that we are not using total number of cows (40), total number of special cows (13) at all. This could be due to wrong wording of just to confuse you. If your questions are different make it clear what exactly you are looking for. To solve a probablity problem the sample space and the selection process should be explicitly mentioned otherwise the question does not make any sense.

Gray_Rhino
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