• April 2nd 2010, 06:53 AM
wideEyedPupil
There's an ad on TV for a news-entertainment show saying there is a 40% chance you have a bought a product containing palm oil. Let's assume they are talking about people buying food products at the supermarket. And let's say they have determined that 40% of food products at the supermarket contain palm oil. If you bought one product you would have 40% of buying a product containing palm oil.

Presumably buying more food products increases one's chances of buying a product containing palm oil. How is this represented mathematically? In 6 years of secondary school maths (including double maths in final years) I always found the translation of real world probability situations into the appropriate equations of permutations and combinations one of the most unclear areas. (Now my problem is I can't even remember all the basic equations and when to apply them). The equations are simple but there application can be tricky.

Please shine some light, mathemagicians. :)
• April 2nd 2010, 10:18 AM
ANDS!
You're talking about two things: probability and "chance". Probabilities are fixed - probability of throwing a 1 when you toss a one sided dice. Probability of winning the lottery. Probability of having a boy or a girl (well this might be affected by a ton of other things - I dunno). In general though, probabilities are something one could calculate without ever having to perform the experiment.

Chance though refers to some observed and studied result. 43% of Americans are against government healthcare. 32% of all white female drives 18-24 will have a car accident this year. Does that mean if I gather three white females 18-24 into a room, one of them is guaranteed to have a car accident? No. That is the difference between "chance" and probabilities: in probabilities an outcome MUST occur. With chance, you could gather 100 females, and not a one will have had an accident. You would EXPECT 32 of them to have had accidents, but it is not a guarantee.

What does that have to do with your question: well what you are describing is more chance than probability. I mean there is a probability a single product will have Ingredient X - 50%. It either does or it doesn't. However the chance someone buys an Ingredient X item is determined by so many things, not the least of which is the volume of product they purchase. How would you represent that mathematically - who knows. Perhaps a linear regression line: as volume of food increased, chance of purchasing Ingredient X product also increases:

$y = \beta _0 \cdot x+\beta_1$

Where "y" would be chance of buying Ingredient X, "x" would be volume of food purchased, and beta 0 and 1 would be slope and y intercept (referrred to as different things when talking about regression, but that is what they are) of this line.

Hopefully that answers (part) of question, or gives some food for thought.
• April 3rd 2010, 01:39 AM
wideEyedPupil
Hi, I guess I'm trying to shoe-horn a complicated situation into a 'theoretically controlled exercise'. Take a situation where one is drawing cards from a shuffled pack. What is the probabilities of drawing a card of the hearts suit. Assuming no jokers, with one draw it is 1in4. Then take another card, assuming the first was not a heart, that leaves 51 cards and 13 of them are hearts, so chance in second draw of a heart is 13/51 and therefore total probability in two draws is 1/4 + 13/51. Is that a correct assumption?

That's actually starting to look like a Fibonacci series of some sort... my maths is so rusty. We used to draw a row of empty boxes, like spreadsheet cells, and write the sequence of probabilities out. Could I just do that to say ten or one hundred purchases. (assuming each product is only bought once and has a 40% probability of containing ingredient x). How can this be represented in a formula. Could you then say N% of a population buying supermarket produce lies within 2 standard deviations of those most likely to consume ingredient x.

Thanks for your equation, ANDS!. I'm giving that some thought, not sure how to use it just yet.

Thanks again
Alastair