BANK & INSURANCE (PROBABILITY) PART 1

Total Questions: 45

41. Ratio of the number of red, blue and black pens in a box is 2:1:3 respectively and the average number of pens in the box is 6. If two pens are drawn at random, then find the probability of getting all the pens are in same color?

Correct Answer: (c) 6/17
Solution:Total number of pens = 6 × 3 = 18 pens
Red pens = 18 × 2/6 = 6 pens
Blue pens = 18 × 1/6 = 3 pens
Black pens = 18 × 3/6 = 9 pens
Required probability = (⁶C₂ + ³C₂ + ⁹C₂)/¹⁸C₂
= (15 + 3 + 36)/153 = 54/153 = 6/17

42. Box A contains 2x red balls, (x + 3) pink balls and x violet balls. If one ball is drawn from the box and the probability of that ball being pink is 2/5, then find the value of x?

Correct Answer: (e) 3
Solution:

(x + 3)C₁ / (2x + x + 3 + x)C₁ = 2/5
8x + 6 = 5x + 15
3x = 9
x = 3

43. In a bag, the average number of red and black balls is 18. If one ball is taken out at random and the probability of getting a red ball is 7/12, then find the number of black balls in the bag?

Correct Answer: (b) 15 balls  
Solution:

Total number of balls (red+black)=18×2=36
Probability of getting a red ball=7/12
x/36=7/12
x=21
Number of black balls=36-21=15 balls

44. A box contains 5 apples and 7 Oranges. If three fruits are drawn in the box without replacement, then what is the probability that the first fruit is apple, second is Orange and third is apple?

Correct Answer: (e) None of these
Solution:

Required probability = 5/12 × 7/11 × 4/10
= 7/66

45. A bag contains 3 red, 2 blue and 4 green balls. 2 balls are drawn randomly from the bag. Find the probability that out of 2 balls at least one ball is blue?

Correct Answer: (b) 5/12  
Solution:

Required probability = ⁷C₁ × ²C₁ / ⁹C₂ + ²C₂ / ⁹C₂
= (14 + 1)/36 = 15/36
= 5/12