# A box contains 11 marbles, 7 red, and 4 green. Five of these marbles are removed at random. If the probability of drawing a green marble is now 0.5, how many red marbles were removed?

Feb 18, 2017

Then number of red marbles removed were $= 4$

#### Explanation:

Given -

Red marbles $= 7$
Green marbles $= 4$
Total no of marbles $= 11$

Number of Marbles removed $= 5$

Marbles in the box $= 11 - 5 = 6$

Probability of drawing one green marble is $= 0.5$

Among the remaining 6 marbles, $x$ number of marbles are green.

Then Probability of drawing one green marble is = number of green marbles / Total Number of marbles.

${P}_{1 g r e e n} = \frac{x}{6}$

We know ${P}_{1 G r e e n} = 0.5$

Then -

$\frac{x}{6} = 0.5$
$x = 0.5 \times 6 = 3$

After 5 marbles are removed from the box, the number of green marbles remaining is 3.

It means out of 4 green marbles, one green marble has been removed.

Out of 5 marbles one marble is green. Then the other four must be red.

Then number of red marbles removed were $= 4$