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Mathematics · 2023 · 4 marks
CBSE 2023 · Region 1 · Set 1 · Q36
There are different types of Yoga which involve the usage of different poses of Yoga Asanas, Meditation and Pranayam as shown in the figure below:…
There are different types of Yoga which involve the usage of different poses of Yoga Asanas, Meditation and Pranayam as shown in the figure below:
The Venn diagram below represents the probabilities of three different types of Yoga, A, B and C performed by the people of a society. Further, it is given that probability of a member performing type C Yoga is $\displaystyle 0 \cdot 44$. 
On the basis of the above information, answer the following questions :
On the basis of the above information, answer the following questions :(i)
Find the value of x .
(ii)
Find the value of $\displaystyle \mathrm{y}$.
(iii)
(a)
Find $\displaystyle \mathrm{P}\left(\frac{\mathrm{C}}{\mathrm{B}}\right)$.
OR
(b)
Find the probability that a randomly selected person of the society does Yoga of type A or B but not C. Case Study - $\displaystyle 2$
Marking-scheme solution
(i)
$\displaystyle \mathrm{x}+0 \cdot 21=0 \cdot 44 \Rightarrow \mathrm{x}=0 \cdot 23$
(ii)
$\displaystyle 0 \cdot 41+\mathrm{y}+0 \cdot 44+0.11=1 \Rightarrow \mathrm{y}=0 \cdot 04$
(iii)
(a)
$\displaystyle \mathrm{P}\left(\frac{\mathrm{C}}{\mathrm{B}}\right)=\frac{\mathrm{P}(\mathrm{C} \cap \mathrm{B})}{\mathrm{P}(\mathrm{B})}$
$\displaystyle \mathrm{P}(\mathrm{B})=0.09+0.04+0.23=0.36$
$\displaystyle \mathrm{P}\left(\frac{\mathrm{C}}{\mathrm{B}}\right)=\frac{0 \cdot 23}{0 \cdot 36}=\frac{23}{36}$
OR
(b)
$\displaystyle \mathrm{P}(\mathrm{A}$ or B but not C$\displaystyle )$
$$\begin{aligned}
& =$\displaystyle 0$ \cdot $\displaystyle 32$+$\displaystyle 0.09$+$\displaystyle 0.04$
& =$\displaystyle 0$ \cdot $\displaystyle 45$
\end{aligned}
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