Answer :
Answer:
The number of red marble to be added in box is [tex]23[/tex].
Step-by-step explanation:
Given that,
Number of red marbles = [tex]16[/tex]
Number of yellow marbles = [tex]7[/tex]
Number of green marbles = [tex]19[/tex]
Total number of marbles in the bag = [tex]42[/tex]
So,
Let the number of red marbles to be added in bag is [tex]x[/tex].
Then Required probability of random drawing a red marble is [tex]\frac{3}{5}[/tex].
[tex]P(E)= \frac{favourable \ outcomes}{total \ number \ of \ outcomes}[/tex]
Here, New number of red marbles is [tex]16+x[/tex]
And total number of marbles be [tex]42+x.[/tex]
∴ [tex]P(red\ marble) = \frac{16+x}{42+x} =\frac{3}{5}[/tex]
⇒ [tex]\frac{16+x}{42+x} =\frac{3}{5}[/tex]
Cross- multiplying we get,
⇒ [tex]5\times (16+x)=3\times (42+x)[/tex]
⇒ [tex]80+5x=126+3x[/tex]
⇒ [tex]2x=46[/tex]
⇒ [tex]x=23[/tex]
thus , the new number of marble to be added in bag is [tex]16+23=39[/tex]
And total number of marble in bag become [tex]42+23=65[/tex].
Hence, The number of red marble to be added in box is [tex]23[/tex].