[UPDATED 2/19/13: added a few more comparisons, and by popular request, appended the list of non-a produce from WordNet.]
On Facebook today, I saw several people referring to a meme "Name a fruit or vegetable that does not contain the letter 'a'." with the comment "not that easy" above it. My immediate thought was that this was silly. Lots of non-a words occurred to me (cherry, lime, plum, beet, celery, turnip, etc., etc.)
But easy or not, the implication behind the challenge is that fruits and vegetables have the letter a so often that counterexamples are hard to think of. That's a testable proposition. We want to know what percentage of English terms for fruits and vegetables contain an a, and how that compares to the overall percentage of nouns with a. In other words, is searching for a non-a item of produce any more difficult than searching for a non-a noun in general.
I wrote a quick Python script to find all the produce (fruits and vegetables) in WordNet* and count how many contained an a compared to the overall frequency of a-containing words. [UPDATE] I also checked a couple of other categories to see how produce compared with medicine names and (non-human) animals. Here are the results:
So not quite 68% of produce terms in English contain the letter a, a clear majority, but essentially identical to the proportion of all English nouns with an a. It should be no harder to find a non-a containing produce term than a non-a containing noun of any other type. Nothing to see here. Move along.
* I counted as a fruit/vegetable any noun that had one of the following synsets in its hypernym path: produce.n.01, edible_fruit.n.01, vegetable.n.01, vegetable.n.02.
Here are all the non-a-containing produce terms identified as such in WordNet. You may thing that some of these terms are "cheating." For example, it contains variant spellings, specific varietal terms for types of fruit where the generic term does have an a, and a few processed foods (e.g., french fries). But I'm not going to skew the list by imposing my own judgment, and the a-containing terms have a similar spread of terms, so I don't think their inclusion really affects the overall percentages, although you may get complaints if you try to use them in response to this question.
|beet||beet green||beetroot||bell pepper|
|berry||bibb lettuce||bilberry||bing cherry|
|blueberry||bok choi||bok choy||bosc|
|brussels sprouts||buttercrunch||celery||celery root|
|chilly||chinese celery||chinese gooseberry||chinese jujube|
|citron||citrous fruit||citrus||citrus fruit|
|cocozelle||cole||common beet||common sorrel|
|dried fruit||edible fruit||eggfruit||elderberry|
|freestone||french endive||french fries||french sorrel|
|globe pepper||golden delicious||gooseberry||green|
|green goods||green groceries||green onion||green pepper|
|greens||grimes' golden||gumbo||hog plum|
|home fries||honeydew||honeydew melon||hot pepper|
|julienne||juneberry||kentucky wonder||key lime|
|net melon||netted melon||newtown wonder||northern spy|
|purple onion||quince||red delicious||red onion|
|sour cherry||sour gourd||soursop||soy|
|summer crookneck||sunchoke||swede||swedish turnip|
|sweet cherry||sweet cup||sweet melon||sweet pepper|
|turnip greens||ugli||ugli fruit||veg|
|veggie||white turnip||whortleberry||wild plum|
|winter cress||winter melon||wintergreen||witloof|
|yellow delicious||yellow mombin||yellow turnip||zucchini|