There are only blue cubes, red cubes and yellow cubes in a box - Edexcel - GCSE Maths - Question 2 - 2019 - Paper 1
Question 2
There are only blue cubes, red cubes and yellow cubes in a box.
The table shows the probability of taking at random a blue cube from the box.
| Colour | blue | r... show full transcript
Worked Solution & Example Answer:There are only blue cubes, red cubes and yellow cubes in a box - Edexcel - GCSE Maths - Question 2 - 2019 - Paper 1
Step 1
Complete the table.
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Answer
To complete the table, we first denote the probability of red cubes as x and the probability of yellow cubes as y. Since the total probability must equal 1:
0.2+x+y=1
We are also told that the number of red cubes is equal to the number of yellow cubes, which translates to their probabilities being equal: x=y.
Substituting y for x, we have:
0.2+2x=1
Solving for x gives:
2x=1−0.22x=0.8x=0.4
Therefore, both the probabilities for red and yellow cubes are 0.4.
Thus, the completed table is:
Colour
blue
red
yellow
Probability
0.2
0.4
0.4
Step 2
Work out the total number of cubes in the box.
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Answer
We know there are 12 blue cubes in the box. Using the probabilities we calculated, we can find the others.
Let the total number of cubes be N.
The number of blue cubes is:
0.2N=12
Thus,
N=0.212=60
Therefore, the total number of cubes in the box is 60.
