CBSE 2023 · Region 2 · Set 2 · Q36 · 4 marks
Recent studies suggest that roughly $\displaystyle 12 \%$ of the world population is left handed.
Depending upon the parents, the chances of having a left handed child are as follows: A : When both father and mother are left handed : Chances of left handed child is $\displaystyle 24 \%$. B : When father is right handed and mother is left handed : Chances of left handed child is $\displaystyle 22 \%$. C : When father is left handed and mother is right handed : Chances of left handed child is $\displaystyle 17 \%$. D : When both father and mother are right handed : Chances of left handed child is $\displaystyle 9 \%$. Assuming that $\displaystyle \mathrm{P}(\mathrm{A})=\mathrm{P}(\mathrm{B})=\mathrm{P}(\mathrm{C})=\mathrm{P}(\mathrm{D})=\frac{1}{4}$ and L denotes the event that child is left handed. Based on the above information, answer the following questions :(i)Find $\displaystyle \mathrm{P}(\mathrm{L} / \mathrm{C})$(ii)Find $\displaystyle \mathrm{P}(\overline{\mathrm{L}} / \mathrm{A})$(iii)Find $\displaystyle \mathrm{P}(\mathrm{A} / \mathrm{L})$Find the probability that a randomly selected child is left handed given that exactly one of the parents is left handed.
Recent studies suggest that roughly $\displaystyle 12 \%$ of the world population is left handed.
Depending upon the parents, the chances of having a left handed child are as follows: A : When both father and mother are left handed : Chances of left handed child is $\displaystyle 24 \%$. B : When father is right handed and mother is left handed : Chances of left handed child is $\displaystyle 22 \%$. C : When father is left handed and mother is right handed : Chances of left handed child is $\displaystyle 17 \%$. D : When both father and mother are right handed : Chances of left handed child is $\displaystyle 9 \%$. Assuming that $\displaystyle \mathrm{P}(\mathrm{A})=\mathrm{P}(\mathrm{B})=\mathrm{P}(\mathrm{C})=\mathrm{P}(\mathrm{D})=\frac{1}{4}$ and L denotes the event that child is left handed. Based on the above information, answer the following questions :
(i)
Find $\displaystyle \mathrm{P}(\mathrm{L} / \mathrm{C})$
(ii)
Find $\displaystyle \mathrm{P}(\overline{\mathrm{L}} / \mathrm{A})$
(iii)
Find $\displaystyle \mathrm{P}(\mathrm{A} / \mathrm{L})$
Find the probability that a randomly selected child is left handed given that exactly one of the parents is left handed.
Marking-scheme solution
(i)
$\displaystyle \mathbf{P}(\mathbf{L} \mid \mathbf{C})=\frac{\mathbf{1 7}}{\mathbf{1 0 0}}$
(ii)
$\displaystyle \mathbf{P}(\overline{\mathbf{L}} \mid \mathbf{A})=\mathbf{1}-\mathbf{P}(\mathbf{L} \mid \mathbf{A})=\mathbf{1}-\frac{\mathbf{2 4}}{\mathbf{1 0 0}}=\frac{\mathbf{7 6}}{\mathbf{1 0 0}}$ or $\displaystyle \frac{\mathbf{1 9}}{\mathbf{2 5}}$
(iii)
$\displaystyle \mathrm{P}(\mathrm{A} \mid \mathrm{L})=\frac{\dfrac{1}{4} \times \dfrac{24}{100}}{\dfrac{1}{4} \times \dfrac{24}{100}+\dfrac{1}{4} \times \dfrac{22}{100}+\dfrac{1}{4} \times \dfrac{17}{100}+\dfrac{1}{4} \times \dfrac{9}{100}}=\frac{24}{72}=\frac{1}{3}$
Or
Probability that a randomly selected child is left-handed given that exactly one of the parents is left handed
$\displaystyle =\mathbf{P}(\mathbf{L} \mid \mathbf{B} \cup \mathbf{C})=\frac{\mathbf{2 2}}{\mathbf{1 0 0}}+\frac{\mathbf{1 7}}{\mathbf{1 0 0}}=\frac{\mathbf{3 9}}{\mathbf{1 0 0}}$
ProbabilityBayes' TheoremApplycase_studymedium
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CBSE Class 12 Mathematics past-paper question from the 2023board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.