Question

Read the following passage and answer the questions given below.

A shopkeeper sells three types of flower seeds A1, A2, A3. They are sold is the form of a mixture, where the proportions of these seeds are 4:4:2 respectively. The germination rates of the three types of seeds are 45%, 60% and 35% respectively.

Based on the above information:

1. Calculate the probability that a randomly chosen seed will germinate.
2. Calculate the probability that the seed is of type A₂, given that a randomly chosen seed germinates.

Answer 1

a. 

Here, P(E₁) = `4/10`, P(E₂) = `4/10`, P(E₃) = `2/10`

`P(A/E_1) = 45/100, P(A/E_2) = 60/100, P(A/E_3) = 35/100`

∴ P(A) = `P(E_1).P(A/E_1) + P(E_2).P(A/E_2) + P(E_3).P(A/E_3)`

= `4/10 xx 45/100 + 4/10 xx 60/100 + 2/10 xx 35/100`

= `180/1000 + 240/1000 + 70/100`

= `490/1000`

= 4.9

b. Required probability = `P(E_2/A)`

= `(P(E_2).P(A/E_2))/(P(A))`

= `(4/10 xx 60/100)/(490/1000)`

= `240/490`

= `24/49`