A box contains red pens and blue pens - Junior Cycle Mathematics - Question 5 - 2017

To find the probability of picking a blue pen, we can use the information given:

The probability of red pens is rac{2}{7}.

Thus, the probability of picking a blue pen is:

P(blue) = 1 - P(red) = 1 - rac{2}{7} = rac{5}{7}

The total number of pens must satisfy the ratio between red and blue pens. Since the number of red pens is rac{2}{7} of the total, the total must be a multiple of 7 to ensure that the number of red pens is an integer. Thus, 20 is not a valid total since it is not a multiple of 7.

Let the original number of red and blue pens be represented in a ratio:

$ext{Ratio of red to blue} = 2:5$

Assuming there are $x$ blue pens, we have:

P(red) = rac{2}{7} ext{ and } P(blue) = rac{5}{7}

When green pens are added, 25% of the total is green. The new total becomes:

rac{75}{100}(x + y) = rac{3}{4} = ext{ total blue and red}

To keep calculations simple, let's say for original pens:

$x + y = 28 ext{ after adding green.}$

After these calculations, we find the chance of picking a blue pen to be:

P(blue) = rac{15}{28}