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 of a randomly chosen seed to germinate

Answer 1

Given that A₁: A₂: A₃ = 4: 4: 2

∴ P(A₁) = `4/10`

P(A₂) = `4/10`

And P(A₃) = `2/10`

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

Let E be the event that a seed germinates and `bar"E"` be the event that a seed does not germinate

∴ `"P"("E"/"A"_1) = 45/100 "P"("E"/"A"_2) = 60/100` and `"P"("E"/"A"_3) = 35/100`

And `"P"(bar"E"/"A"_1) = 55/100, "P"(bar"E"/"A"_2) = 40/100` and `"P"(bar"E"/"A"_3) = 65/100`

P(E) = `"P"("A"_1)*"P"("E"/"A"_1) + "P"("A"_2)*"P"("E"/"A"_2) + "P"("A"_3)*"P"("E"/"A"_3)`

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

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

= `490/1000`

= 0.49