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Salad probability question

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Leela stops to get some food at Fishy Joe's and she sees that 40% of the salads have cheese topping on them, 20% have ranch on them, and 40% are plain. Of the salads with cheese topping, 45% have "froot" on them; of the salads with ranch, 15% have "froot" on them; and of the plain salads, only 10% have froot on them. Leela tells the clerk to choose a salad for her at random. Given that the salad does not have "froot", what is the probability that it is a plain salad?

Apr 27th, 2015

P(pl|nf) = P(nf|Pl)P(pl)/P(nf) = 0.9*0.4/(P(nf|pl)*pl+P(nf|ch)P(ch)+P(nf|ra)P(ra)) 

=0.36/(0.36+0.55*0.4+0.85*0.20) = 0.36/(0.36+0.22+0.17) = 0.48

Apr 27th, 2015

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