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. Which arrow shows the probability that this crayon is (i) blue, (ii) yellow, (iii) not black. (b) Darren buys 16 more crayons that are either blue or red. He puts these in the box with the 20 crayons he already has. He now picks a crayon at random from the box. The probability that he picks a blue crayon is even. How many red crayons did he buy?

GCSE OCR Maths Probability: Darren has these 20 crayon in a

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

Question 8

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. Which arrow shows the probability that t... show full transcript

Worked Solution & Example Answer: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

Step 1

(a)(i) Arrow

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Answer

The probability of drawing a blue crayon is calculated as follows:

The number of blue crayons is 8 out of a total of 20 crayons. Therefore, the probability is given by:

$P(blue) = \frac{8}{20} = 0.4$

The corresponding arrow on the diagram should point to 0.4.

Step 2

(a)(ii) Arrow

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Answer

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.

Step 3

(a)(iii) Arrow

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Answer

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.

Step 4

(b) How many red crayons did he buy?

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Answer

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.

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

Worked Solution & Example Answer: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

(a)(i) Arrow

(a)(ii) Arrow

(a)(iii) Arrow

(b) How many red crayons did he buy?

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