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Question
Read the following passage and answer the questions given below.
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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.
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Based on the above information:
- Calculate the probability that a randomly chosen seed will germinate.
- Calculate the probability that the seed is of type A2, given that a randomly chosen seed germinates.
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Solution
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`
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Given that P(A) = `square`, P(C) = `square`
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P(L) = P(A ∩ L) + P(C ∩ L) + P(T ∩ L)
`="P"("A")*"P"("L"//"A") + "P"("C")*"P"("L"//"C") + "P"("T")*"P"("L"//"T")`
`= square * square + square * square + square * square`
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`"P"("C"//"L") = ("P"("L" ∩ "C"))/("P"("L"))`
= `("P"("C") * "P"("L"//"C"))/("P"("L"))`
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