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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
Solution
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
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