Question

Please help me I have been stuck on this question for ages

Answer 1

Answer:28 green and 35 red

Step-by-step explanation:

Given

If there are r red counter and g green counter then

Probability of drawing a green counter is $P(g)=\frac{4}{9}$

and $P(g)=\frac{\text{No of g counter}}{\text{Total no of counter}}$

Thus $\frac{\text{No of g counter}}{\text{Total no of counter}}=\frac{4}{9}$

$\frac{g}{g+r}=\frac{4}{9}$

$\Rightarrow 9g=4g+4r$

$\Rightarrow 5g=4r\quad \ldots(i)$

Also if 4 red and 2 green counter is added the probability of drawing a green counter is

$P(g)=\frac{10}{23}=\frac{\text{No of g counter}}{\text{Total no of counter}}$

$\Rightarrow \frac{10}{23}=\frac{g+2}{g+2+r+4}$

$\Rightarrow \frac{10}{23}=\frac{g+2}{g+r+6}$

$\Rightarrow 10g+10r+60=23g+46$

$\Rightarrow 10r+14=13g\ quad \ldots(ii)$

Substitute the value of g in equation (ii)[/tex]

$\Rightarrow 10\times \frac{5}{4}g+14=13g$

$\Rightarrow \frac{25}{2}g+14=13g$

$\Rightarrow g=28$

Therefore $r=35$

Thus there 28 green counter and 35 red counter