40% of our total crop is apples. 60% of our total crop is berries. 20% of our total crop are apples harvested in winter. 20% of our total crop are apples harvested in summer. Can we find the percentage of total winter crops?

I have sketched out a probability tree, probability tables, and tried to work through Bayes Rule approaches but feel that there is not enough information to calculate the total percentage of winter crops without knowing the percentage of berries grown in winter or summer. Am I missing something here or do we need more information to know the percentage of winter crops?

  • $\begingroup$ You don't miss anything. We need more information. $\endgroup$ Aug 24 '21 at 14:31
  • $\begingroup$ Thank you Abdoul! $\endgroup$
    – pi89eIP
    Aug 24 '21 at 14:45

The given information is

Apples Berries Total
Summer 20% ? ?
Winter 20% ? ?
Total 40% 60% 100%

From this we cannot find the proportion of berries harvested in summer or winter, or the proportion of total summer vs winter crops. All we can say is that at least 20% of the total crops are winter crops.

If one of the statements about apples was instead a statement about berries in summer or winter, then we could solve the problem.

  • $\begingroup$ Thank you David! Really appreciate your help on this. $\endgroup$
    – pi89eIP
    Aug 24 '21 at 14:44

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