A boy has a collection of balls of different colours. He has a total of 35 balls in his basket out of which seven are black in colour and eight are yellow in colour. Out of remaining balls, some are white and the rest are red. Based on the above, answer the following questions: (a) If the probability of drawing a red ball at random from the basket is three times that of a white ball, then find the number of red balls in the basket. (b) Find the probability of drawing a ball at random from the basket which is either a black or a white ball.

 A boy  has a collection of balls of different colours. He has a total of 35 balls in his basket out of which seven are black in colour and eight are yellow in colour. Out of remaining balls, some are white and the rest are red.

Based on the above, answer the following questions:

(a) If the probability of drawing a red ball at random from the basket is three times that of a white ball, then find the number of red balls in the basket.

(b) Find the probability of drawing a ball at random from the basket which is either a black or a white ball

Total balls = 35

Number of Black balls = 7

Number of Yellow balls = 8

Remaining balls = 35 − 7 − 8 = 20  

Let number of white balls = w

Let number of red balls = r 

Given that 

Out of remaining balls, some are white and the rest are red.

Remaining balls =  20  

w + r  =  20  ---------[1]

Given 

P(red) = 3 × P(white) 

 P(red) = r/35

P(white) = w/35 

 r/35 = 3 × w/35

r = 3w  ---------(2) 

 Put (2) in (1)

w + r  =  20

w + 3w = 20

4w = 20

w = 5  

use r = 3w 

 r = 3 × 5 = 15 

 Number of red balls = 15

Number of  Black balls = 7

Numbe r of White balls [w] = 5  

 Number of  favourable outcomes = 7 + 5 = 12  

P(black or white) = 12/35

foe more details use the video 

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A survey was conducted on the patients who have undergone knee replacement surgeries. It was found that, Robotic Knee replacement surgeries have 90% success rate. On a particular day, robotic surgery was performed on three patients, A, B and C, one after the other. Assuming that the success and failure of each surgery is independent of each other, find the probability that : (i) exactly one surgery is successful, (ii) at most two surgeries are successful. probability of independent events cbse 12th maths old board exam question paper 2025 2026 independent events success failure type

 A survey was conducted on the patients who have undergone knee replacement surgeries. It was found that, Robotic Knee replacement surgeries have 90% success rate. On a particular day, robotic surgery was performed on three patients, A, B and C, one after the other. Assuming that the success and failure of each surgery is independent of each other, find the probability that : (i) exactly one surgery is successful, (ii) at most two surgeries are successful. probability of independent events cbse 12th maths old board exam question paper 2025 2026 independent events success failure type

Given:

 P(Success) = 90% = 0.9 = 9/10

 P(Failure) = 1 − 0.9 = 0.1 = 1/10

let S debite Success,

 F denote Failure

Probability that exactly one surgery is successful

possibilities SFF, FSF, FFS

P(SFF) = 0.9 × 0.1 × 0.1 = 0.009

P(FSF) = 0.1 × 0.9 × 0.1 = 0.009

P(FFS) = 0.1 × 0.1 × 0.9 = 0.009

  P(exactly one auccess) = 0.009 + 0.009 + 0.009 = 0.027 = 27/1000 

 Probability that at most two surgeries are successful

At most two successes means 0 or 1 or 2 successes

so

 Probability that at most two surgeries are successful 

= 1 − P(all three successful)

= 1 - P[ SSS]

= 1 - [0.9 × 0.9 × 0.9]

 = 1 -  0.729 

= 0.271 

= 271/1000

see this video for more explanation 

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