Darren has these 20 crayon in a box: - 8 blue - 4 red - 5 black - 3 green (a) He chooses a crayon at random from the box - OCR - GCSE Maths - Question 8 - 2019 - Paper 2

There are no yellow crayons in the box, thus the probability of selecting a yellow crayon is:

$P(yellow) = \frac{0}{20} = 0$

The arrow for this probability should point to 0.

To find the probability of drawing a crayon that is not black, we first find the total number of non-black crayons. There are:

• 8 blue
• 4 red
• 3 green

This amounts to:

$8 + 4 + 3 = 15$

Thus, the probability of selecting a crayon that is not black is:

$P(not \ black) = \frac{15}{20} = 0.75$

The arrow should, therefore, point to 0.75.

Let the number of red crayons Darren bought be denoted as ( r ). After buying these, the total number of crayons becomes:

• Total blue (8) + Total red (4 + r)

The total number of crayons is then:

$20 + 16 = 36$

Darren's probability of selecting a blue crayon is:

$P(blue) = \frac{8}{36}$

To find an even probability, we will set an equation:

$\frac{8}{36} = \frac{r + 4}{36}$

Solving this shows:

$8 = r + 4$

Thus, re-arranging gives:

$r = 8 - 4 = 4$

Therefore, Darren bought 4 red crayons.