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 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?​

Answer 1

Answer:

>11 ÷ 50 , probability

Answer 2

★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

_______________