There are 12 counters in a bag. There are an equal number of red counters, blue counters and yellow counters in the bag. There are no other counters in the bag. 3 counters are taken at random from the bag. (a) Work out the probability of taking 3 red counters. The 3 counters are put back into the bag. Some more counters are put into the bag. There is still an equal number of red counters, blue counters and yellow counters in the bag. There are no counters of any other colour in the bag. 3 counters are taken at random from the bag. (b) Is it now less likely or equally likely or more likely that the 3 counters will be red? You must show how you get your answer.

GCSE Edexcel Maths Probability: There are 12 counters in a bag.

There are 12 counters in a bag - Edexcel - GCSE Maths - Question 21 - 2017 - Paper 2

Question 21

There are 12 counters in a bag. There are an equal number of red counters, blue counters and yellow counters in the bag. There are no other counters in the bag. 3 c... show full transcript

Worked Solution & Example Answer:There are 12 counters in a bag - Edexcel - GCSE Maths - Question 21 - 2017 - Paper 2

Step 1

Work out the probability of taking 3 red counters.

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Answer

To find the probability of taking 3 red counters from a total of 12 counters where there are equal numbers of red, blue, and yellow counters, we first determine the number of each color counter.

Since there are 12 counters and they are equally divided into red, blue, and yellow, we have:

Red counters: 4
Blue counters: 4
Yellow counters: 4

The probability of drawing 3 red counters can be computed using combinations:

Total ways to choose 3 counters from 12: $inom{12}{3} = \frac{12!}{3!(12-3)!} = \frac{12 \times 11 \times 10}{3 \times 2 \times 1} = 220$
Ways to choose 3 red counters from 4: $\binom{4}{3} = \frac{4!}{3!(4-3)!} = \frac{4}{1} = 4$

Thus, the probability is:

$P(3 \text{ red}) = \frac{\binom{4}{3}}{\binom{12}{3}} = \frac{4}{220} = \frac{1}{55}$

Step 2

Is it now less likely or equally likely or more likely that the 3 counters will be red?

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Answer

After some counters are put back into the bag, the situation changes but we still have equal numbers of red, blue, and yellow counters. The probability calculation remains the same since the proportions of each color are unchanged.

The probability of drawing 3 red counters remains:

$P(3 \text{ red}) = \frac{1}{55}$

Now we need to compare this with the probability of drawing 3 counters in general. Given that the total number of counters has increased but the ratio remains equal among colors, the likelihood of drawing 3 of any specific color retains its proportionality.

Thus, we conclude:

It is neither less likely nor more likely; it is equally likely that the 3 counters drawn will be red.

There are 12 counters in a bag - Edexcel - GCSE Maths - Question 21 - 2017 - Paper 2

Worked Solution & Example Answer:There are 12 counters in a bag - Edexcel - GCSE Maths - Question 21 - 2017 - Paper 2

Work out the probability of taking 3 red counters.

Is it now less likely or equally likely or more likely that the 3 counters will be red?

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