There are only blue counters, yellow counters, green counters and red counters in a bag. A counter is taken at random from the bag. The table shows the probabilities of getting a blue counter or a yellow counter or a green counter. | Colour | blue | yellow | green | red | |-----------|------|--------|-------|------| | Probability | 0.2 | 0.35 | 0.4 | ? | (a) Work out the probability of getting a red counter. (b) What is the least possible number of counters in the bag? You must give a reason for your answer.

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

There are only blue counters, yellow counters, green counters and red counters in a bag - Edexcel - GCSE Maths - Question 10 - 2017 - Paper 3

Question 10

There are only blue counters, yellow counters, green counters and red counters in a bag. A counter is taken at random from the bag. The table shows the probabilitie... show full transcript

Worked Solution & Example Answer:There are only blue counters, yellow counters, green counters and red counters in a bag - Edexcel - GCSE Maths - Question 10 - 2017 - Paper 3

Step 1

Work out the probability of getting a red counter.

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Answer

To find the probability of getting a red counter, we first note that the total probability of all outcomes must equal 1. Hence, we can express the probability of getting a red counter as follows:

Let the probability of getting a red counter be denoted as $P(r)$ . Given the probabilities for other colors:

$P(blue) + P(yellow) + P(green) + P(red) = 1$

Substituting the known values:

$0.2 + 0.35 + 0.4 + P(r) = 1$

Calculating the sum of the probabilities:

$0.2 + 0.35 + 0.4 = 0.95$

Therefore, we have:

$0.95 + P(r) = 1$

Solving for $P(r)$ :

$P(r) = 1 - 0.95 = 0.05$

Thus, the probability of getting a red counter is 0.05.

Step 2

What is the least possible number of counters in the bag? You must give a reason for your answer.

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Answer

To find the least possible number of counters in the bag, let the number of counters of each color be denoted as follows:

Let $b$ be the number of blue counters,
Let $y$ be the number of yellow counters,
Let $g$ be the number of green counters,
Let $r$ be the number of red counters.

Since the probability of getting a red counter is $0.05$ , we can express this as:

$P(r) = \frac{r}{b + y + g + r} = 0.05$

This implies:

$r = 0.05(b + y + g + r)$

For $r$ to be a whole number, the factor $b + y + g + r$ must be a multiple of 20. Thus, the least value fulfilling this requirement occurs when:

$b + y + g + r = 20$

Given that the minimum counts of each color must also be positive integers, the least number of counters required in total is, therefore, 20.

There are only blue counters, yellow counters, green counters and red counters in a bag - Edexcel - GCSE Maths - Question 10 - 2017 - Paper 3

Worked Solution & Example Answer:There are only blue counters, yellow counters, green counters and red counters in a bag - Edexcel - GCSE Maths - Question 10 - 2017 - Paper 3

Work out the probability of getting a red counter.

What is the least possible number of counters in the bag? You must give a reason for your answer.

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