A shopkeeper sells three types of flower seeds A1, A2 and A3.
Question:

A shopkeeper sells three types of flower seeds A1, A2 and A3. 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.

Solution:

Given that: A1: A2: A3 = 4: 4: 2

So, the probabilities will be

P(A1) = 4/10, P(A2) = 4/10 and P(A3) = 2/10,

Where A1, A2 and A3 are the three types of seeds.

Therefore, the required probability is 16/51 or 0.314.