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 Ratio Analysis and Problem Solving: 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 recognize that the sum of the probabilities of all possible outcomes must equal 1. Therefore, we can set up the equation:

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

Substituting the known probabilities:

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

Calculating the sum of the probabilities of blue, yellow, and green:

$0.2 + 0.35 + 0.4 = 0.95$

Now substituting back into the equation:

$0.95 + P(red) = 1$ $P(red) = 1 - 0.95 = 0.05$

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

Step 2

What is the least possible number of counters in the bag?

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Answer

To find the least possible number of counters in the bag, we need to consider the probabilities calculated previously. The probability of getting a red counter is 0.05, which can be expressed in terms of the total number of counters, denoted as N.

Therefore, we have:

$P(red) = \frac{number\ of\ red\ counters}{N} = 0.05$

This implies that the number of red counters must be at least:

$number\ of\ red\ counters = 0.05N$

Since the number of counters must be a whole number, we can rearrange the equation. For the smallest whole number, N must be a multiple of 20 (since 0.05 of 20 is 1).

Thus, the least possible number of counters in the bag that satisfies this condition is 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?

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