**Toolbox:**

- The mixture of \(A_1\;A_2\;A_3\) type seeds is \(4:\;4:\;2\)
- Let \(E_1 \;seeds \;selected \;is\;A_1\)
- Let \(E_2 \;seeds \;selected \;is\;A_2\)
- Let \(E_3\;seeds \;selected \;is\;A_3\)
- \(A\;the\; seeds\;germinates\)
- P(A)=P(\(E_1\))P(\(A/E_1\))+p(\(E_2\))P(\(A/E_2\))+P(\(E_3\))P(\(A/E_3\))
- P(\(\bar{A}/E_1\))=1-P(A/\(E_1\))
- P(\(\bar{A}/E_2\))=1-P(A/\(E_2\))
- P(\(\bar{A}/E_3\))=1-P(A/\(E_3\))
- P(\(E_2\bar{A}\))=\(\Large\frac{{P(E_2)}{P(\bar{A}/E_2)}}{{p(E_1)}{p(\bar{A}/E_1)}+{P(E_2)}{P(\bar{A}/E_2)}+{(P(E_3)}{P(\bar{A}/E_3)}}\)

P(\(E_1\))=\(\large\frac{4}{10}\)=\(\frac{2}{5}\) \(seeds\; 'A'\;is\; settled\)

P(\(E_2\))=\(\large\frac{4}{10}\)=\(\frac{2}{5}\) \(seeds\; 'A_2'\;is\; settled\)

P(\(E_3\))=\(\large\frac{2}{10}\)=\(\frac{1}{5}\) \(seeds\; 'A_3'\;is\; settled\)

P(\(A/E_1\))=P(germinates/\(A_1\) selected)

=\(\large\frac{45}{100}\)

P(\(\bar{A}/E_1\))=\(\frac{55}{100}\)

P(\(A/E_2\))=P(germinates/\(A_2\) selected)

=\(\large\frac{60}{100}\)

P(\(\bar{A}/E_2\))=\(\large\frac{40}{100}\)

P(\(A/E_3\))=P(germinates/\(A_3\) selected)

=\(\large\frac{35}{100}\)

P(\(\bar{A}/E_3\))=\(\large\frac{65}{100}\)

P(A)=P(germinates)

=\(\Large\frac{2}{5}\)\(\times\)\(\frac{45}{100}\)+\(\frac{2}{5}\)\(\times\)\(\frac{60}{100}\)+\(\frac{1}{5}\)\(\times\)\(\frac{35}{100}\)

=\(\large\frac{245}{500}\)=0.49

P(\(\bar{A}/E_3\))=P(does not germinate/seed \(A_3\) is selected)

=\(1-\large\frac{35}{100}\)=\(\large\frac{65}{100}\)

=\(0.65\)

P(\(E_2/\bar{A}\))=P(seeds\(A_2\) is chosen/the seeds does not germinate)

=\(\Large\frac{\frac{2}{5}\times\frac{40}{100}}{\frac{2}{5}\times\frac{55}{100}+\frac{2}{5}\times\frac{40}{100}+\frac{1}{5}\times\frac{65}{100}}\)

=\(\Large\frac{\frac{4}{25}}{\frac{110+80+65}{500}}\)

=\(0.314\)