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Probability Old Exam P Forum 

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#1




Multiplication Theorem of Probability
A psychology experiment on memory was conducted which required participants to note which songs they found pleasing. Based on many results, the (partial) probability distribution below was determined for the discrete random variable X = number of songs found pleasing (during a fixed time period).
X = # songs 1 2 3 4 5 6 7 8 9 10 Probability 0 0.02 0.04 0.07 0.15 0.18 0.24 0.14 0.11 0.05 Given that the person finds at least 7 songs pleasing to the ear, what is the probability that they find 8 songs pleasing to the ear? Please round to the second decimal point. Should it be = 0.14/(0.24+0.14+0.11+0.05) or = 0.14/(0.24+0.14) 
#6




For an actual exam question, there would have been many reviewers discussing the wording, so it would likely be precise. Exam P and most of the prelims have pilot questions that don't count, where imprecise wording might inadvertently slip through many reviewers. If it is a real question on P, then it has been given before, and I hope they would have seen an unexpected cluster of wrong answers that would tell them to rethink the wording. But I don't know the actual process, and defective questions could still get through.

#9




IMO, as worded, I would interpret it as "(exactly) eight". If the intent would be to answer "either 8 or 9 or . . .", then the wording would be required to indicate it as such.
With that said, as Gandalf points out, there are cases of typos and forgotten wording, but I would expect that (exactly) eight should be the correct answer given the wording, regardless of intent.
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