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A box contains 150 oranges.If one orange is taken out from the box at random and the probability of its being rotten is 0.06, then find the number of good oranges in the box.

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Number of bad ones: $150\cdot 0.06=9$? –  Mårten W Jan 31 '13 at 16:06
Strictly speaking, we don't know the number of good oranges. There could be 150 bad oranges in the box. We can only give the estimated number of good oranges. –  akkkk Jan 31 '13 at 16:07
@akkkk: We are told that if we take an orange at random from this box, the probability of bad is $0.06$. It follows that there are for sure exactly $9$ bad. –  André Nicolas Jan 31 '13 at 16:18
@MårtenW 0.06 is the probability of a rotten one. The question asks for the number of good ones, thus $150 \times (1 - 0.06) = 141$. –  Michael Jan 31 '13 at 17:01
@AndréNicolas: I read it as a "factory of boxes" question, in which some process generates uniformly distributed rotten oranges. If you know the probability for this exact box, then apparently you have already counted the rotten ones. –  akkkk Jan 31 '13 at 19:34

1 Answer 1

The probability that the orange is not rotten (good) is $1 - 0.06 = 0.94$. Hence, we know that $0.94$ times the total number of oranges ($150$) is the number of good oranges, which numerically is $150 \times 0.94 =141$.

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But answer at the back of the book is 91. –  Nye Sain Jan 31 '13 at 16:10
Are you sure. If yes then Thanks. –  Nye Sain Jan 31 '13 at 16:15
@nye The answer can be $91$ if and only if good does not mean not bad in your question. –  Parth Kohli Jan 31 '13 at 16:17
The math in @Novice's answer is sound, and I'm sure that's the solution that the text book author had in mind. But strictly speaking it is not accurate to assert that there are 9 bad oranges in the box, because the question specifically states that one orange was removed from the box. Therefore, there are only 149 oranges left in the box. So there were 9 bad apples at the start of the problem, but the question remains: was the apple that was removed bad or not? (If it was bad, there are indeed still 141 good oranges in the box; if it was good, then, since it has now been removed, there a –  kmote Jan 31 '13 at 17:02
It are oranges g –  Michael Jan 31 '13 at 17:03

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