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 Ratio Analysis and Problem Solving: 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 that a counter taken at random from the box will be green

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Answer

Given that the probability of drawing a blue counter is 0.4, we can find the probability of drawing a green counter by the following calculation:

Let the probability of a red counter be denoted as $P(R)$ . Thus, we have: $P(B) + P(R) + P(G) = 1$ Substituting $P(B) = 0.4$ we get: $0.4 + P(R) + P(G) = 1$ Thus, $P(R) + P(G) = 0.6$

Step 2

The ratio of red counters to green counters

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Answer

We know the ratio of the number of red counters (R) to green counters (G) is 7:8. Therefore, we can express this as: $\frac{R}{G} = \frac{7}{8}$ This implies: $R = \frac{7}{8}G$

Step 3

Estimating the number of green counters

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Answer

Now, we can substitute the expression for R into the earlier equation: $\frac{7}{8}G + G = 0.6$ This simplifies to: $\frac{15}{8}G = 0.6$ From which we can solve for G: $G = 0.6 \times \frac{8}{15} = 0.32\text{ (total number of green counters in the box)}$

Now, to find the expected number of times Sameena takes a green counter in 50 draws: $\text{Expected number of green counters} = P(G) \times 50 = \frac{0.32}{50} \times 50 = 16$

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 that a counter taken at random from the box will be green

The ratio of red counters to green counters

Estimating the number of green counters

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