A bag contains in all 80 balls. Some of them are white, some are blue and some are red. The number of white balls is 12 times the number of blue balls. The number of red balls is less than the number of white balls but more than the number of blue balls. If one ball is selected at random from the bag, what is the probability that it is red ?

Answer

The probability that the ball selected at random is res is `19/40.`

Explanation

Let the number of blum b alls be x. Then the number of white ball is 12x. The total number of balls is 80.
`therefore` the number of red balls `=(80-13x).`
From the given condition
`12x gt (80 -13x) gtx`
(i) `12x gt 80 -13xtherefore12x+13xgt80 therefore25x gt80therefore x gt (80)/(25)therefore x gt 3 (1)/(5)" "...(1)`
(ii) `80-13xgt x therefore80 gt x +13x therefore80 gt14x`
`therefore14xlt 80 thereforex lt(80)/(14)thereforex lt5(5)/(7)" "...(2)`
From (1) and (2) `x gt 3(1)/(5)` but less than `5(5)/(7).`
`thereforex=4`
The number of red balls `=80-13x=80-13xx4=80-42=38`
`therefore` the number of red balls is 38.
`(R)=(n(R))/(n(S))" "thereforeP(R)=(38)/(80)" "thereforeP(R)=(19)/(40).`