. Suppose a man is standing trial accused of being an apple thief (A). The prose
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Question
. Suppose a man is standing trial accused of being an apple thief (A). The prosecution shows video evidence of the man stealing bananas (B) and presents the following (inductive) argument: “The case against the accused thief is very strong, it is very likely he is an apple thief. Here is why... we know that only 1 in 100 people are banana thieves and people who don’t steal bananas tend not to steal apples – only 1 in 20. But, banana thieves are 10 times more likely to steal apples than non-banana thieves! And, we have seen the evidence that the accused definitely IS a banana thief. Therefore, he is an apple thief as well.” (a) Is this argument inductively strong? Explain your answer. (b) How confident should the jury be (given only this argument) that the accused is an apple thief? Explain your answer.
Explanation / Answer
(a) Here if we talk inductively, the argument is very strong here. As there is very high chance of a person who is a banana theif, will steal apple too as compared to those who not steal banana. It is a simple case of induction where we infere that A causes B and B causes C then C will be caused by A.
(b) HEre the jury will also go statisitically that the probability of stealing an apple thief by a banana theif.
Pr(Apple thief l banana thief) = Pr(banana theif) * Pr(apple theif l banana theif) = 1/100 * 10 * Pr(apple theif l not banana theif) = 1/100 * 10 * [ 1- Pr(not apple thief l not banana thef)] = 1/100 * 10 * 19/20 = 19/200 = 0.095
that probability is greater than 0.05 so yes the jury should accuse that the given person is an apple thief.
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