(3 points) A farmer is preparing to sow seeds in the field. He is sowing three s

Question

(3 points) A farmer is preparing to sow seeds in the field. He is sowing three seed varieties, and each has a different probability of germinating. All three varieties are loaded into a seed drill, which will be used to plant the seeds in the field.

Calculate the probability of a randomly-selected seed being:

a) Germinated

b) Of type A given that it is germinated

c) Of type C given that it is not germinated

If you could please explain your reasoning I would appreiate it! for part a I got 66.5%, and for part b I got 18.8%. Do you think that's correct?

For part C since it's asking for not germinated, would it looks something like this?    P(AlG') = (P(C)xP(GlC'))/(P(G')) ?  

So [probability type C x (1-prob type C germinating) ] / (1-total germination rate) ? That's what I was thinking but will really appreciate an explanation. Thank you!

Explanation / Answer

a) probability of a randomly-selected seed being:Germinated

=P(from A and germinated+from B and germinated+from C and germinated)

=0.25*0.5+0.45*0.8+0.3*0.6=0.665 (correct)

b) P(type A|germinated) =P(from A and germinated)/P(germinated) =0.25*0.5/0.665=0.188 (correct)

c) here also ur reasoning is correct:

P(type C|not germinated) =P(C and not germinated)/P(not germinated) =(0.3*(1-0.6))/(1-0.665)=0.3582

( please revert for any clarification required)

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