A shopkeeper sells three types of flower seeds \[{{A}_{1}}\], \[{{A}_{2}}\] and \[{{A}_{3}}\]. They are sold as a mixture where the proportions are \[4:4:2\] respectively. The germination rates of the three types of seeds are \[45%\], \[60%\] and \[35%\]. Calculate the probability (i) of a randomly chosen seed to germinate (ii) that it will not germinate given that the seed is of type A3, (iii) that it is of the type A2 given that a randomly chosen seed does not germinate.
Given that: \[{{A}_{1}}:\text{ }{{A}_{2}}:\text{ }{{A}_{3}}~=\text{ }4:\text{ }4:\text{ }2\]
So, the probabilities will be
\[P({{A}_{1}})\text{ }=\text{ }4/10,\text{ }P({{A}_{2}})\text{ }=\text{ }4/10\]and \[P({{A}_{3}})\text{ }=\text{ }2/10\],
Where \[{{A}_{1}}\], \[{{A}_{2}}\] and \[{{A}_{3}}\].are the three types of seeds.
Therefore, the required probability is \[16/51\] or \[0.314\].
