# Rohit Jaspreet and Alia appeared for an interview

Q 2: Rohit Jaspreet and Alia appeared for an interview for three vacancies in the same post. The probability of Rohit’s selection is 1/5, Jaspreet’s selection is 1/3 and Alia’s selection is 1/4. The event of selection is independent of each other.                 [CBSE  2024]

Based on the above information, answer the following question :

(i) What is the probability that at least one of them is selected ?                (1)

(ii) Find where G is the event of Jaspreet’s selection and denotes the event that Rohit is not selected.                  (1)

(iii) Find the probability that exactly one of them is selected.                      (2)

OR

(iii) (b) Find the probability that exactly two of them are selected.          (2)

Solution:-

(i) The probability of Rohit’s selection P(R)=  1/5

The probability of Jaspreet’s selection P(J) = 1/3

The probability of Alia’s selection P(A)= 1/4

The probability of Rohit is not selected P(R’)=  1 – 1/5 = 4/5

The probability of Jaspreet is not selected P(J’)=  1 – 1/3 = 2/3

The probability of Alia is not selected P(A’)=  1 – 1/4 = 3/4

The probability that at least one of them is selected = 1 – P(None of them is selected)

= 1 – P(R’∩J’∩A’)

= 1 – P(R’)×P(J’)×P(A’)

= 1 – 2/5

= 3/5

Thus, The probability that at least one of them is selected is 3/5

(ii) Since, where G is the event of Jaspreet’s selection and denotes the event that Rohit is not selected.

The probability of Jaspreet’s selection P(G) = 1/3

The event of selection is independent of each other then

NOW,

(iii) From eq(i)

The probability of Rohit’s selection P(R)=  1/5

The probability of Jaspreet’s selection P(J) = 1/3

The probability of Alia’s selection P(A)= 1/4

The probability of Rohit is not selected P(R’)=  1 – 1/5 = 4/5

The probability of Jaspreet is not selected P(J’)=  1 – 1/3 = 2/3

The probability of Alia is not selected P(A’)=  1 – 1/4 = 3/4

The probability that exactly one of them is selected = P(R)×P(J’)×P(A’) + P(R’)×P(J’)×P(A) + P(R’)×P(J)×P(A’)

Thus, the probability that exactly one of them is selected = 7/15

OR

(iii) (b) The probability that exactly two of them are selected = P(R)×P(J)×P(A’) + P(R)×P(J’)×P(A) + P(R’)×P(J)×P(A)

Thus, the probability that exactly two of them are selected = 3/20

Q 1:- An instructor at the astronomical centre shows three among the brightest stars in a particular constellation. Assume that the telescope is located at O(0, 0, 0) and the three stars have their locations at the points D, A and V having position vectors and respectively.

Based on the above information, answer the following question:

(i) How far is the star V from star A ?                         (1)

(ii) Find a unit vector in the direction of .            (1)

(iii)(a) Find the measure of ∠VDA .                    (2)

OR

(iii) (b) What is the projection of vector on vector ?               (2)

Solution :- See full solution

Q 3:- A store has been selling calculators at Rs 350 each. A market survey indicates that a reduction in price (p) of calculator increases the number of units (x) sold. The relation between the price and quantity sold is given by the demand function .                       [CBSE  2024]

Based on the above information, answer the following questions:

(i) Determine the number of units (x) that should be sold to maximise the revenue R(x) = xp(x). Also, verify result.                                   (2)

(ii) What rebate in price of calculator should the store give to maximise the revenue ?                 (2)

Solution:- See full solution