CBSE 2023 · Region 1 · Set 1 · Q36 · 4 marks
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 :(i)Find the value of x .(ii)Find the value of $\displaystyle \mathrm{y}$.(iii)Find $\displaystyle \mathrm{P}\left(\frac{\mathrm{C}}{\mathrm{B}}\right)$.Find the probability that a randomly selected person of the society does Yoga of type A or B but not C. Case Study - $\displaystyle 2$
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)
Find $\displaystyle \mathrm{P}\left(\frac{\mathrm{C}}{\mathrm{B}}\right)$.
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)
$\displaystyle \mathrm{P}\left(\frac{\mathrm{C}}{\mathrm{B}}\right)=\frac{\mathrm{P}(\mathrm{C} \cap \mathrm{B})}{\mathrm{P}(\mathrm{B})}$
$\displaystyle \mathrm{P}(\mathrm{B})=0.09+0.04+0.23=0.36$
$\displaystyle \mathrm{P}\left(\frac{\mathrm{C}}{\mathrm{B}}\right)=\frac{0 \cdot 23}{0 \cdot 36}=\frac{23}{36}$
$\displaystyle \mathrm{P}(\mathrm{A}$ 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}
ProbabilityConditional ProbabilityApplycase_studymedium
More from Probability
- Assertion: Two coins are tossed simultaneously. The probability of getting two heads, if it is known that at…2023 · asked 3×
- A shop selling electronic items sells smartphones of only three reputed companies A, B and C because chances…2025 · asked 3×
- Smoking increases the risk of lung problems. A study revealed that 170 in 1000 males who smoke develop lung…2026 · asked 3×
- The probability distribution of a random variable X is: where k is some unknown constant. The probability…2024 · asked 3×
- Recent studies suggest that roughly 12 % of the world population is left handed. Depending upon the parents,…2023 · asked 3×
- Two balls are drawn at random from a bag containing 2 red balls and 3 blue balls, without replacement. Let…2022 · asked 3×
- Let X be a random variable which assumes values x 1, x 2, x 3, x 4 such that 2 P(X=x 1)=3 P(X=x 2)=P(X=x 3)=5…2022 · asked 3×
- The probability distribution of a random variable X is given below: (i) Find the value of k. (ii) Find P(1 ≤…2023 · asked 3×
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.