Probability Leo pulled out pencils from his pencil case and then put them back in 30 times.he record the results in this chart: orange:7,purple 15, black 5,green3

Question

If had 10 pencils in his pencil case,how many of each coloured pencil is he likely to have in his pencil case?

Answer 1

So Vicky T.,

You must take real, noisy data and figure the most likely contents of the pencil case. This is not so bad, because it follows your intuition exactly! Since Leo has 30 results, you might expect the pencil colors to "come up" proportionally to the number of pencils of each color in the case. So let's start with the most obvious: the purple came up 15/30 times, that is the same proportion as 5/10, so there are (most likely) to be 5 purple pencils. Similarly, for green, 3/30 is the same proportion as 1/10, so there is most likely to be only one green pencil. That leaves 4 pencils to be split between orange and black. Is it likely for there only to be one black and three orange, yet randomly draw a 5:7 split? No, that would be quite unreasonable (though not impossible!). But, if there were two each black and orange, then they might easily come up 5:7. After all, that is just getting an orange instead of the black expected, for one drawing.

Now, can you also calculate the probability of actually GETTING a 7:15:5:3 drawing, with a 2:5:2:1 content? That is quite a different problem, and calculates what are called combinations of results. You will eventually be able to do that. The probability is actually quite small! But, it is greater than the probability of getting that result with any other content.

-- Cheers, -- Mr. d.