A bag contains 50 balls.Some of them are white,blue and red. The number of white balls is 11 times the blue balls.The number of red balls is less than the white balls but more than the blue balls. If one ball is taken out at random from the bag. What is the probability that is a red ball.
Answers
Answer:
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 .