Probability of Shirts...
The soccer team's shirts have arrived in a big box, and people just start grabbing them, looking for the right size. The box contains 4 medium, 10 large, and 6 extra-large shirts. You want a medium for you and one for your sister. Find the probability of the event(s) described below:
d) At least one of the first four shirts you check is a medium.
*I have done this problem at least 5 times, and every time I keeping seeing a different way to look at it*
Here are my rationales:
1) Since they are asking for the chance of getting one out of 4, it would be the bare minimum chance of getting it, so it would be X,X,X, Y. Doing that you get 4/17 or ~23%. (I do not know exactly if this violates the "at least" rule, since it makes sense that you are going for the least common amount).
2) This was my friends method, seems like permutation to me:
1/5, 0, 0 0 = 20%
4/5, 4/19, 0, 0 = (4/5)*(4/19) = 16.8%
4/5, 15/19, 4/18, 0 = (4/5)*(15/19)*(4/18) = 14.3%
4/5, 15/19, 14/18, 4/17 = (4/5)*(15/19)*(14/18)*(4/17) = 11.5%
20 + 16.8 + 14.3 + 11.5 = 62.6%
3) I honestly cannot remember the other 3 ways I was doing it, but one was like 86% so I know that is wrong.
I am doing this purely as guesto-mechanics, and I have no idea what I am looking at or doing, so please if you get the answer try to explain in common sense what is going on so I can get it (Giggle).
Thank you for your detailed response Archie Meade. Where can I get reasoning like yours lol! I assume I had read the question wrong then, hehe :).
Originally Posted by Archie Meade
This may be out of the scope of your class but you can use the hypergeometric probability mass function to solve this problem quite simply:
Total number of shirts=N=20, total number of shirts you check=n=4, total number of medium size shirts=k=4, X= the number of medium shirts you find
You're looking for the probability that at least 1 for the four shirts you looked at is size medium.
So, Pr(X 1)
But this is the same as 1-Pr(X<1), and because X can't be negative, this can be rewritten as 1-Pr(X=0)
So using the hypergeometric PMF:
Haha thats an awesome formula Sun. Geez I feel like a toddler now lol :P. Never even considered matrices for this problem, let alone stats.
Originally Posted by downthesun01