Need a hint for the second part of this question (probability) Watch

pineapplechemist
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Fruit trees produce a crop which is graded class 1, class 2.1, class 2.2 or class 3. Overall the proportion of fruit in the four categories is 1/8, 2/8, 3/8 and 2/8 respectively. But this includes fruit coming from the 1/3 of trees that are not properly watered. A tree that is underwatered produces fruit of inferior quality with the proportion in the four classes being 1/10, 2/10, 4/10, and 3/10.
(i) What is the probability a fruit is classed as 2.1 if it is produced by a tree that is known to have been properly watered?
(ii) What is the probability that a fruit classed as 2.1 has come from a properly watered tree?

I got11/40 for the first part. For the second part i'm trying to compute P(A given B) where A is the event the fruit comes from a properly watered tree and B is the event the fruit is classed 2.1. This gives me (11/40)/(2/8) = 1.1. Where is my mistake here?
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tombayes
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(Original post by pineapplechemist)
Fruit trees produce a crop which is graded class 1, class 2.1, class 2.2 or class 3. Overall the proportion of fruit in the four categories is 1/8, 2/8, 3/8 and 2/8 respectively. But this includes fruit coming from the 1/3 of trees that are not properly watered. A tree that is underwatered produces fruit of inferior quality with the proportion in the four classes being 1/10, 2/10, 4/10, and 3/10.
(i) What is the probability a fruit is classed as 2.1 if it is produced by a tree that is known to have been properly watered?
(ii) What is the probability that a fruit classed as 2.1 has come from a properly watered tree?

I got11/40 for the first part. For the second part i'm trying to compute P(A given B) where A is the event the fruit comes from a properly watered tree and B is the event the fruit is classed 2.1. This gives me (11/40)/(2/8) = 1.1. Where is my mistake here?
use bayes theorem and use part (i).
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pineapplechemist
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(Original post by tombayes)
use bayes theorem and use part (i).
Thanks, got it
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Phichi
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(Original post by tombayes)
use bayes theorem and use part (i).
I have this feeling this was your moment to shine, with the username and all
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