A bag contains in all 180 balls. Some of them are white, some are blue and some are red. The number of white balls is 12 times the number of blum balls. The number of red balls is less than the number of white balls but more than the number of blub balls. IF one ball is selected at random from the bag, what is the probability that it is red ?

Answer

The probability is `( 7)/( 25)`

Explanation

Let the number of blue balls of x.
Then the number of white balls is 11x …...(From the given conditon )
Total number of balls is 50. …(Given )
`:. ` the number of red balls `= ( 50 - 12x ) `
As per the given condition , `11x gt ( 50 - 12x ) gt x `
(a) `11x gt 50 - 12x " " :. 11x + 12x gt 50" " 23x gt 50`
`:. x gt ( 50)/( 23)` i.e. ` x gt 2 (4)/(23)` ...(1)
(b) `50 - 12x gt x " " :. 50 gt x + 12 x " " 50 gt 13 x " "` i.e. `13x lt 50`
`:. x lt ( 50)/( 13) ` `" ":. x lt 3 (11)/( 13)` ...(2)
From (1) and (2) , ` x gt 2(4)/(23)` but less than `3 (11)/(13)`
`:. x = 3 `
The number of red balls `= 50 - 12x = 50 -12 xx 3 `
`= 50 - 36 = 14 `
`:. n (R ) = 14 `
The probability of taking at randoma red ball `=P (R )`
`P ( R ) = ( n (R ))/( n (S)) = (14)/( 50)`
`:. P (R ) = ( 7)/( 25)`