Skip to content

There are different types of… (Class 12 Maths 2023, Q36)

questionbuddy.in/q/cbse-12-maths-2023-65-1-1-q36-different-types-yoga-involve-usage

MathsCBSE Class 12 · Board exam 2023, set 65/1/1 · 4 marks · Case-based

CBSE Class 12 Mathematics 2023: question 36

Set in the CBSE Class 12 board exam of 2023, paper 65/1/1, section E, question 36, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q36 · 4 marks · Case-basedCompetency-basedProbability

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 0·44.

On the basis of the above information, answer the following questions :

  1. (i)

    Find the value of x.

    1 mark
  2. (ii)

    Find the value of y.

    1 mark
  3. (iii)(a)

    Find .

    2 marks

  4. OR

    (iii)(b)

    Find the probability that a randomly selected person of the society does Yoga of type A or B but not C.

    2 marks

Figure in the paper: First figure: picture listing Types of Yoga: Anusara, Kundalini, Vinyasa, Bikram, Hatha Yoga. Second figure: Venn diagram in sample space S with three overlapping ovals A, B, C in a row. Regions: A only 0·32, A∩B 0·09, B only y, B∩C x, C only 0·21; outside all sets 0·11. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 65/1/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

The C oval is made up of two regions, x and 0.21.

Hint 2

For y, use the fact that all regions of S together have probability 1.

Hint 3

For conditional probability, divide the overlap of B and C by the whole of B. For (iii)(b), list the regions inside A or B that lie outside C.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

  1. (i) , so .

    1 mark

  2. (ii) The probabilities of all regions add to 1: , so and .

    1 mark

  3. (iii)(a) , with .

    1 mark

  4. (iii)(a) , so .

    1 mark

  5. (iii)(b) The person is in A or B but not in C. These regions are A only, A∩B and B only. So .

    1½ marks

  6. (iii)(b) .

    ½ mark

Answer: (i) x = 0.23; (ii) y = 0.04; (iii)(a) 23/36; (iii)(b) 0.45

Where the marks are

  • (i) (1 mark)
  • (ii) Total probability 1 gives (1 mark)
  • (iii)(a) (1 mark)
  • (iii)(a) (1 mark)
  • (iii)(b) Adds the regions (1½ marks)
  • (iii)(b) Answer 0.45 (½ mark)

Revise the chapter

Practise this chapterBoard-style questions from Probability, one at a time, marked against the answer key and marking points.Back to the full paper2023 board paper, set 65/1/1: every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.