Question

A bag contains in all 50 balls. Some of them are white, some are blue

and some are red. The number of white balls is 11 times the number of blue balls. The number of red balls is less than the number of white

balls. Also, the number of red balls is more than the number of blue

balls. If one of the balls is selected at random from the bag, what is the

probability that it is red ?

Answer 1

Answer:

Probability of getting a red ball = 14/50 = 0.28

Step-by-step explanation:

W + B + R = 50

Let the number of blue balls be x.

Therefore, W = 11x, B = x and R = 50-12x

The no of red balls is less than no of white balls. Hence,  

R < W

50-12x < 11x

50 < 23x

x > 50/23

x > 2.17 (First condition)

It is also given that the no of red balls is more than the no of blue balls. Hence,

R > B

50-12x > x

50 > 13x

x < 50/13

x < 3.84 (Second condition)

Putting the two conditions together:

2.17< x < 3.84

Since x has to be an integer, therefore, x = 3.

Therefore, number of blue balls is 3. Number of red balls is 50-12(3) = 14.

Therefore, probability of getting a red ball = 14/50 = 0.28

Answer 2

Answer:

The probability getting red ball = 7/25

Step-by-step explanation:

Let 'x' be the number of blue balls

then number of white balls = 11x

x + 11x = 12x

Therefore sum of blue and white balls = 12x (multiple of 12)

It is also given that,

x < number of red balls < 11x

The possible sum of blue and white balls are,

12,24,36,48

case 1). if 12, blue = 1 and white = 11x = 11 then red = 38 > white

case 2). if 24, blue= x = 2 white  11x = 22 then red = 26 > white

case 3). if 36, blue= x = 3 white  11x =33 then red = 14 < white

case 4 ). if 48, blue= x = 4 white  11x = 44 then red = 2 < red

Therefore case 3) is the correct possibility.

blue = 3, white = 33 and Red = 14

Find the probability

Total ball = 50

red ball = 14

probability getting red ball = 14/50 = 7/25