A shopkeeper sells three types of flower seeds \(A_1\), \(A_2\), \(A_3\). 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% respectively. Calculate the probability in the following cases.
The probability that seed will not germinate, given that the seed is of type \(A_3\).
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\displaystyle\frac{65}{100}\)
Let G be the event that the seed germinates. The germination rate of type \(A_3\) is 35%, so \(P(G \mid A_3) = 0.35\). Not germinating is the complementary event:
\(P(G' \mid A_3) = 1 - 0.35 = 0.65\)
\( \displaystyle = \frac{65}{100} \)
The proportions of the mixture are not needed here, because the seed is already known to be of type \(A_3\).
NCERT Exemplar:
Probability
