CBSE 2022 · Region 3 · Set 1 · Q14 · 4 marks
A shopkeeper sells three types of flower seeds A1, A2, A3. They are sold in the form of a mixture, where the proportions of these seeds are $\displaystyle 4$ : $\displaystyle 4$ : $\displaystyle 2$, respectively. The germination rates of the three types of seeds are $\displaystyle 45$%, $\displaystyle 60$% and $\displaystyle 35$% respectively.
Based on the above information :(a)Calculate the probability that a randomly chosen seed will germinate;(b)Calculate the probability that the seed is of type A2, given that a randomly chosen seed germinates.
A shopkeeper sells three types of flower seeds A1, A2, A3. They are sold in the form of a mixture, where the proportions of these seeds are $\displaystyle 4$ : $\displaystyle 4$ : $\displaystyle 2$, respectively. The germination rates of the three types of seeds are $\displaystyle 45$%, $\displaystyle 60$% and $\displaystyle 35$% respectively.
Based on the above information :
(a)
Calculate the probability that a randomly chosen seed will germinate;
(b)
Calculate the probability that the seed is of type A2, given that a randomly chosen seed germinates.
Marking-scheme solution
\(\displaystyle E_{1}\) : Seed is of type \(\displaystyle A_{1}\)
\(\displaystyle E_{2}\) : Seed is of type \(\displaystyle A_{2}\)
\(\displaystyle E_{3}\) : Seed is of type \(\displaystyle A_{3}\)
A: Seed germinates
\[\begin{aligned}
& P\left(E_{1}\right)=\frac{4}{10}, P\left(E_{2}\right)=\frac{4}{10}, P\left(E_{3}\right)=\frac{2}{10} \\
& P\left(A \mid E_{1}\right)=\frac{45}{100}, P\left(A \mid E_{2}\right)=\frac{60}{100}, P\left(A \mid E_{3}\right)=\frac{35}{100}
\end{aligned}
\]
\[\begin{aligned}
& P\left(E_{1}\right)=\frac{4}{10}, P\left(E_{2}\right)=\frac{4}{10}, P\left(E_{3}\right)=\frac{2}{10} \\
& P\left(A \mid E_{1}\right)=\frac{45}{100}, P\left(A \mid E_{2}\right)=\frac{60}{100}, P\left(A \mid E_{3}\right)=\frac{35}{100}
\end{aligned}
\]ProbabilityBayes' TheoremApplycase_studymedium
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CBSE Class 12 Mathematics past-paper question from the 2022board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.