There are only blue counters, red counters and green counters in a box. The probability that a counter taken at random from the box will be blue is 0.4. The ratio of the number of red counters to the number of green counters is 7:8. Sameena takes at random a counter from the box. She records its colour and puts the counter back in the box. Sameena does this a total of 50 times. Work out an estimate for the number of times she takes a green counter.

GCSE Edexcel Maths Probability: There are only blue counters, re

There are only blue counters, red counters and green counters in a box - Edexcel - GCSE Maths - Question 19 - 2022 - Paper 3

Question 19

There are only blue counters, red counters and green counters in a box. The probability that a counter taken at random from the box will be blue is 0.4. The ratio o... show full transcript

Worked Solution & Example Answer:There are only blue counters, red counters and green counters in a box - Edexcel - GCSE Maths - Question 19 - 2022 - Paper 3

Step 1

The probability of green counters

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Answer

Let the total number of counters be represented as $N$ . According to the problem, the probability of selecting a blue counter is 0.4. Therefore, the probability of not selecting a blue counter, which consists of red and green counters, is:

$P(R ext{ or } G) = 1 - P(B) = 1 - 0.4 = 0.6$

Let the number of red counters be represented as $R$ and green counters as $G$ . From the given ratio of red to green counters, we can write:

$\frac{R}{G} = \frac{7}{8}$

This implies that:

$R = \frac{7}{8}G$

Thus, the total number of red and green counters is:

$R + G = \frac{7}{8}G + G = \frac{15}{8}G$

Now we also know that:

$R + G = 0.6N$

Therefore, we can substitute for $R$ :

$\frac{15}{8}G = 0.6N$

Step 2

Finding the number of green counters

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Answer

To express $G$ in terms of $N$ , rearranging gives:

$G = \frac{8}{15} (0.6N) = \frac{4.8}{15} N$

Now, the expected number of times Sameena picks a green counter can be calculated using the estimation:

Since she picks a counter 50 times:

$E(G) = 50 \times P(G)$

To find the probability of picking a green counter, we need to determine $P(G)$ :

Since red and green counters together are 0.6 of the total, and their ratio is 7:8, we have:

The total parts in the ratio = 7 + 8 = 15 parts.
Hence, the probability of picking a green counter is:

$P(G) = \frac{8}{15 \times 0.6} = \frac{8}{9}$

So the expected number of green counters picked:

$E(G) = 50 \times \frac{8}{15 \times 0.6} = \frac{50 \times 8}{15} = \frac{400}{15} = 26.67$

Thus, Sameena is expected to take approximately 27 green counters.

There are only blue counters, red counters and green counters in a box - Edexcel - GCSE Maths - Question 19 - 2022 - Paper 3

Worked Solution & Example Answer:There are only blue counters, red counters and green counters in a box - Edexcel - GCSE Maths - Question 19 - 2022 - Paper 3

The probability of green counters

Finding the number of green counters

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