Probability that product A occurs on the same order as Product B

Hello all,

Here is my question:

We know three things.
1) A store sells three and only three products (Bread, Milk and Cheese).
2) In total the store has sold a quantity of 100, but we don't know what the breakdown is. It could be 30 loaves of bread, 20 slices of cheese and 50 jugs of milk, for example, but we don't know. All we know is that the store has sold a total quantity of 100.
3) The store has only even received 15 orders. Each order could include one product, two, or all three, and we do not know what quantity of each product appeared on each order. It could be that one order was for 5 loaves of bread, 2 cheeses and 1 milk. Another could be just 10 loaves of bread. We don't know. But we know there have been 15 orders so far.

What is the raw probability that Milk will appear on the same order as cheese? In other words, out of the 15 orders we have taken, what percent of them will have both milk and cheese on the order?

John

John123 said:

Hello all,

Here is my question: ..... Excellent ... now where is your answer?!

We know three things.
1) A store sells three and only three products (Bread, Milk and Cheese).
2) In total the store has sold a quantity of 100, but we don't know what the breakdown is. It could be 30 loaves of bread, 20 slices of cheese and 50 jugs of milk, for example, but we don't know. All we know is that the store has sold a total quantity of 100.
3) The store has only even received 15 orders. Each order could include one product, two, or all three, and we do not know what quantity of each product appeared on each order. It could be that one order was for 5 loaves of bread, 2 cheeses and 1 milk. Another could be just 10 loaves of bread. We don't know. But we know there have been 15 orders so far.

What is the raw probability that Milk will appear on the same order as cheese? In other words, out of the 15 orders we have taken, what percent of them will have both milk and cheese on the order?

John

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What are your thoughts?

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Subhotosh Khan said:

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33

Click to expand...

thanks for your reply. I'm basically stuck at the beginning. I don't even know if its possible to find the answer from the details. I start by thinking the raw probability will be 33.33% of a particular product appearing on an order, because there are three products (so 33.3% each). So I'm thinking the answer to the probability of an order having two products is 66.66%. But then I realize that your probability is different when we're talking multiple products, and so I think I need to use the total number of quantity sold somehow. So I'm thinking I need to calculate the total number of possibilities of order combinations. If we had one product it would be 100 (products) x 15 (orders), so 1500. But if we have three products we need to multiply by 3. so 1500 x 3 = 4500. We may have to take 3 or something to ensure all products have been accounted for. And now we have the total combinations (I think).

But how many of these possible combinations will have two or more products? I don't know. But whatever it is, I take it we can divide it by 2 to get the number of combinations with milk and cheese. So we can do

100 / total number of combinations (about 4500) * total number of combinations with 2 or more products / 2