Question 1196181
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If the basket is empty after we select the last red apple, then the last apple selected is red.<br>
We can represent any sequence of apples selected by a string like "GGRG...RRGR" containing 72 "R"s and 15 "G"s.  Then the probability in question is the probability that the last letter in the string is "R".<br>
Since there are 72 red apples and 15 green apples, the probability that the last one selected is red is 72/(72+15) = 72/87.<br>
ANSWER: 72/87<br>
For a more thorough demonstration of why that is the answer, use the basic definition of probability:<br><pre>
         number of favorable outcomes
  P = -----------------------------------
       total number of possible outcomes</pre>
In this problem the possible outcomes are all the possible arrangements of the 72 "R"s and 15 "G"s, which is<br>
{{{(87!)/((72!)(15!))}}}<br>
And, because the favorable outcomes are those with a red apple last, the number of favorable outcomes is the number of ways of arranging 71 of the 72 red apples and all 15 of the green ones, which is<br>
{{{(86!)/((71!)(15!))}}}<br>
Then the probability in the question is<br>
{{{((86!)/((71!)(15!)))/((87!)/((72!)(15!))) = (86!/87!)(((72!)(15!))/((71!)(15!)))=72/87}}}<br>
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Note added after seeing the response from tutor @ikleyn....<br>
Her math is nearly always very good; but her English is not.  The statement of the problem clearly says that the basket must be empty after removing the 72nd red apple.<br>