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 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 form the bag what is the probability that it is red?
Answers
Answer:
>11 ÷ 50 , probability
★Given:-
- No.of.balls in a bag = 50
- Some are white, blue & red
- No of white balls = 11 ×no of blue balls
- No of red balls < no of white balls
- No of red balls > no of blue balls
★To find:-
- If one of the balls is selected at random form the bag what is the probability that it is red?
★Solution:-
Let, no.of.blue balls = x
Then,no.of.white balls = 11x
Sum of blue balls&white balls:-
⇒Blue balls + White balls
⇒ x + 11x = 12x
Given that,
- Blue balls < Red balls < White balls
⇒x < no of red balls < 11x
As the total no.of.balls = 50,
The possible sum of blue and white balls are:
⇒ 12, 24, 36, 48
Case - 1:-
If the sum is 12,
Blue ball = 1 i.e, x = 1
White ball = 11x = 11×1 = 11
Red ball = 50 - 12 = 38
Number of Red ball > White ball
(38 > 11 )
But given that,
- No of red balls < no of white balls
Hence,It does not satisfy the given condition
Case - 2:-
If sum is 24 ,
Blue ball = 2 i.e, x = 2
White = 11×2 = 22
Red ball = 50 - 24 = 26
Number of Red ball > White ball
(26>22)
But given that,
- No of red balls < no of white balls
Again,It does not satisfy the given condition
Case - 3:-
If sum = 36 ,
Blue ball = 3 i.e,x = 3
White ball = 11×3 = 33
Red ball = 50 - 36 = 14
Number of Red ball < White ball(14<33)
Number of Red ball > Blue ball (14>3)
Hence, this satisfies the given condition
Case - 4:-
If sum = 48 ,
Blue ball = 4i.e, x = 4
White ball = 11 × 4 = 44
Red ball = 50 - 48 = 2
Number of Red ball < White ball
Number of red ball < Blue ball
Hence, it does not satisfy the given condition
We can see, correct possibility is in the 3rd case where total sum = 36
Therefore,
Number of blue balls = x =3,
Number of white balls:
⇒ 11x = 11(3) =33
Number of Red balls = 14
We know:-
✦Probability=No.of.possible outcomes/Total no.of.outcomes
We have:
- No.of.red balls = 14
- Total no of balls = 50
Putting the values,
→Probability of getting red ball:
⇒ 14/50 = 7/25
Hence,
The probability of getting red ball from the bag is 7/25
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