Question

a bag contains 16 red marbles, 7 yellow marbles, and 19 green marbles. how many additional red marbles must be added to the 42 marbles already in the bag so that the probability of randomly drawing a red marble is 3/5

Answer 1

The number of red marble to be added in box is
`23`.

Explanation:

Given that,

Number of red marbles =
`16`

Number of yellow marbles =
`7`

Number of green marbles =
`19`

Total number of marbles in the bag =
`42`

So,

Let the number of red marbles to be added in bag is
`x`.

Then Required probability of random drawing a red marble is
`(3)/(5)`.

`P(E)= (favourable \ outcomes)/(total \ number \ of \ outcomes)`

Here, New number of red marbles is
`16+x`

And total number of marbles be
`42+x.`

∴
`P(red\ marble) = (16+x)/(42+x) =(3)/(5)`

⇒
`(16+x)/(42+x) =(3)/(5)`

Cross- multiplying we get,

⇒
`5* (16+x)=3* (42+x)`

⇒
`80+5x=126+3x`

⇒
`2x=46`

⇒
`x=23`

thus , the new number of marble to be added in bag is
`16+23=39`

And total number of marble in bag become
`42+23=65`.

Hence, The number of red marble to be added in box is
`23`.