Question 1089452: there are 200 pieces of cookies in a bag, 15% of which are wrapped. If 80% of the pieces of cookie are oatmeal, which is the smallest number of wrapped oatmeal pieces that could be in the bag? plz show the work
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! there are 200 pieces of cookies in a bag.
15% are wrapped.
this means that .15 * 200 = 30 are wrapped.
80% of the cookies are oatmeal.
this means that .8 * 200 = 160 are oatmeal.
this also means that .2 * 200 = 40 are not oatmeal.
since 30 are wrapped, and there are more than 30 cookies that are not oatmeal, then it is entirely feasible that none of the wrapped cookies are oatmeal, unless i'm not understanding the problem correctly.
if you were to randomly pick cookies to be wrapped, then it's a different story.
you would pick 30 cookies to be wrapped without looking at them.
the probability that you would pick an oatmeal cookie would be .8 because 80% of the cookies in the batch are oatmeal.
the probability that you would pick a cookie that's not oatmeal would be .2 because 20% of the cookies in the batch are not oatmeal.
the smallest number of oatmeal cookies that are wrapped would still be 0 and the probability of that happening if you are picking randomly would be:
40/200 * 39/199 * 38/198 * 37/197 ...... 11/171
i worked it out in excel and got 2.069.... * 10^-27
another formula would be c(40,30) / c(200,30) = 2.069..... * 10^-27
both give you the same answer, but the combination formula combined with the use of a calculator is much easier.
bottom line is that it is possible to get 0 oatmeal cookies wrapped if you pick cookies out of the batch randomly, but the probability that they will all not be oatmeal is extremely small.
the full answer from my TI-84 plus calculator is that the probability that all the wrapped cookies are not oatmeal when you pick the cookies out of the batch randomly is 2.06907098 * 10^-27
that's a very small probability.
it's so small that if you rounded the answer to 26 decimal digits, it would be equal to 0.
but it's not zero, and therefore it is possible that you could get zero wrapped cookies that are oatmeal if you picked them out of the batch randomaly without looking at them.
if you looked, and you could tell the difference, then there's no question that you could pick 30 cookies to be wrapped that are not oatmeal since you would have 40 to pick from.
that's my take.
15% wrapped = 30
20% not oatmeal = 40
30 wrapped could all be not oatmeal.
|
|
|
