Probability and percentage

Question

if there is 500 people and there were 39 apples, what is the percentage of 5 people getting an apple

Answer 1

Hi Meeshanth B.,

So many holes in this question --

let's start with grammar. 500 people "are", not "is"; why "were" rather than "are" for the apples, did they disappear?; were the apples randomly distributed intact to members of the crowd; there is no percentage, but rather a probability, of a result as stated; are the 5 people picked at random to check; should they have ONLY one apple among them, or can they have any number up to 39? If should have only 1 apple, and randomly distributed/selected, then do by successive multiplications of probability of NO apples for each of the first 5 people examined. As it were, you approach the answer from the backside. Note that the people selected decrease the universe for distributing further apples, because this is a successive conditional calculation. So when you say, person #1 had that probability for "failure" (no apples), they are then out of the distribution calculations for the rest! The terms to multiply start as (461/500)*(460/499) etc.

It is useful to note something here: if you started calculating ways for the group of 5 to have one apple, then ways to have 2 apples, and so on, up to all the ways 39 apples could be distributed across 500 people, you would have no possibility of typing in formulas for calculation without making an error, and you would eventually go nuts. So therefore, it is always indicated to calculate the probability of "success" as 1 - probability(failure), where failure here means, NO apples among any of the 5 people examined. It is far easier to calculate NOT getting ANY apples.

-- Cheers, --Mr. d.