A shopkeeper sells three types of seeds `A_1, A_2a n dA_3` They are sold as a mixture where the proportions are 4:4:2 respectively. The germination rate of three types of seeds are 45%, 60% and 35%. Calculate the probability (i)that it will germinate given that the seed is of type `A_3` . (ii)of a randomly chosen seed to germinate. (iii)That it is of type `A_2` given that a randomly chosen seed does not germinate.

Explanation

`P(A_{1})=frac{4}{10}, P(A_{2})=frac{4}{10} and P(A_{3})=frac{2}{10}`
.

Let E be the event that a seed will germinate and (E’) be
the event that a seed will not germinate.

`therefore P(E / A_{1})=frac{45}{100}, P(E / A_{2})=frac{60}{100} and P(E / A_{3})=frac{35}{100}`

and `P((E’) / A_{1})=frac{55}{100}, P((E’) / A_{2})=frac{40}{100} and P((E’) / A_{3})=frac{65}{100}`

(i) `P(E)=P(A_{1}) cdot P(E / A_{1})+P(A_{2}) cdot P(E / A_{2})+P(A_{3}) cdot P(E / A_{3})`

`=frac{4}{10} cdot frac{45}{100}+frac{4}{10} cdot frac{60}{100}+frac{2}{10} cdot frac{35}{100} `

...