The probability of getting the red ball from the bag is 7 / 25

Let the number of blue balls be ' x '

According to question,

The number of WHITE balls is 11 times the number of Blue Ball

Therefore, number of white balls = 11x

So,

Blue balls + White balls = x + 11x = 12x

ALSO, it is given :

The number of red balls is less than the number of white balls and is more than the number of Blue Balls, that is,

Blue balls < Red balls < White balls

x < number of red balls < 11x

Since the total number of balls are 50,

The POSSIBLE sum of blue and white balls are :

12, 24, 36, 48

If the sum is 12,

Blue ball = 1 [ x = 1 ]

White = 11×1 = 11

Red ball = 50 - 12 = 38

Since Number of Red ball > White ball

It does not satisfy the given condition

if sum is 24

Blue ball = 2 [ x = 2 ]

White = 11×2 = 22

Red ball = 50 - 24 = 26

Again Since Number of Red ball > White ball

It does not satisfy the given condition

Taking sum = 36

Blue ball = 3 [ x = 3 ]

White = 11 * 3 = 33

Red ball = 50 - 36 = 14

Since Number of Red ball < White ball and also Number of Red ball > Blue ball

So this SATISFIES the condition

Taking sum = 48

Blue ball = 4 [ x = 4 ]

White = 11 * 4 = 44

Red ball = 50 - 48 = 2

Since Number of Red ball < White ball but Number of red ball < Blue ball

So, it does not satisfy the given condition

Therefore third option where total sum is 36 is the only correct possibility.

So,

Number of blue balls = 3,

Number of white balls = 33

Number of Red balls = 14

We know ,

Total number of ball = 50

Number of red ball = 14

Probability = Number of possible OUTCOMES / Total number of outcomes

Probability of getting red ball = 14/50 = 7/25

Hence,

The probability of getting red ball from the bag is 7/25