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There are 9 counters in a bag - Edexcel - GCSE Maths - Question 17 - 2017 - Paper 1

Question 17

There are 9 counters in a bag. 7 of the counters are green. 2 of the counters are blue. Ria takes at random two counters from the bag. Work out the probability th... show full transcript

Worked Solution & Example Answer:There are 9 counters in a bag - Edexcel - GCSE Maths - Question 17 - 2017 - Paper 1

Step 1

Calculate Total Combinations

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Answer

To determine the total number of ways Ria can take two counters from the bag, we use the combination formula:

$C(n, r) = \frac{n!}{r!(n - r)!}$

Here, ( n = 9 ) (total counters) and ( r = 2 ) (counters taken).

Calculating:

$C(9, 2) = \frac{9!}{2!(9 - 2)!} = \frac{9 \times 8}{2 \times 1} = 36$

Thus, there are a total of 36 ways to take 2 counters from 9.

Step 2

Calculate Successful Combinations

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Answer

To find the number of successful outcomes (one green and one blue counter), we calculate:

Ways to choose 1 green counter from 7:
$C(7, 1) = 7$
Ways to choose 1 blue counter from 2:
$C(2, 1) = 2$

Thus, the number of successful outcomes is:

$7 \times 2 = 14$

Step 3

Calculate the Probability

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Answer

The probability ( P ) that Ria takes one counter of each colour is given by the ratio of successful outcomes to total combinations:

$P = \frac{\text{Successful Outcomes}}{\text{Total Combinations}} = \frac{14}{36} = \frac{7}{18}$

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