Question

A bag contains 15 balls of which x are blue and the remaining are red. If the number of red balls is increased by 5, the probability of drawing the red ball doubles find
(i) P(red ball)
(ii) p(blue ball)
(iii) P(blue ball if 5 red balls are actually added).

Answer 1

Total balls $=15$

$P\left(Red\right)=\frac{15-x}{15}P\left(Blue\right)=\frac{x}{15}$

when $5$ red balls are added

$\left(\frac{15-x}{15}\right)\times 2=\frac{20-x}{20}$

$600-40x=300-15x$

$300=25x$

$x=12$

There are $12$ blue balls and $3$ red balls

$P\left(redballs\right)=\frac{3}{15}=\frac{1}{5}P\left(blueballs\right)=\frac{12}{15}=\frac{4}{5}$

$P$(blue ball if $5x$ balls are actually added)$=1-2\times \left(\frac{1}{5}\right)=\frac{3}{5}$