A bag contains 150 counters. The counters are either red or yellow. (a) Riley picks a counter from the bag, records its colour, and replaces it. They do this nine times. Here are Riley’s results. Red NN Yellow IIII Use Riley’s results to work out how many red counters are likely to be in the bag. (b) Ling uses the same bag of counters and picks the counters in the same way. Here are Ling’s results. Red NN II Yellow NN III Use Ling’s results to estimate the probability of choosing a red counter from the bag. Give your answer as a fraction in its simplest form. (c) Explain why Ling’s results are likely to give a better estimate of the probability of choosing a red counter from the bag than Riley’s results.

Photo AI

A bag contains 150 counters - OCR - GCSE Maths - Question 19 - 2023 - Paper 3

Question 19

A bag contains 150 counters. The counters are either red or yellow. (a) Riley picks a counter from the bag, records its colour, and replaces it. They do this nine t... show full transcript

Worked Solution & Example Answer:A bag contains 150 counters - OCR - GCSE Maths - Question 19 - 2023 - Paper 3

Step 1

Use Riley's results to work out how many red counters are likely to be in the bag.

96%

114 rated

Answer

Riley picked a total of 9 counters. Out of these, 3 were red and 6 were yellow. To find the estimated number of red counters in the bag, we can set up a proportion:

Let the number of red counters be $R$ .

The probability of picking a red counter based on Riley's results is: $P(Red) = \frac{3}{9} = \frac{1}{3}$

Since there are a total of 150 counters, we can express this proportionately:

$\frac{R}{150} = \frac{1}{3}$

Cross-multiplying gives:

$R = \frac{150}{3} = 50$

Therefore, there are likely to be 50 red counters in the bag.

Step 2

Use Ling's results to estimate the probability of choosing a red counter from the bag.

99%

104 rated

Answer

Ling picked a total of 9 counters (4 red and 5 yellow). The probability of picking a red counter based on Ling's results is: $P(Red) = \frac{4}{9}$

Hence, the estimated probability of choosing a red counter from the bag is $\frac{4}{9}$ .

Step 3

Explain why Ling's results are likely to give a better estimate of the probability of choosing a red counter from the bag than Riley's results.

96%

101 rated

Answer

Ling's results may provide a better estimate of the probability because:

Larger Sample Size: Though both samples were 9, the distribution of colors may better reflect the actual ratio in Ling’s set since counter-distribution can vary per selection sequence.
Variability: Riley's results indicated a substantial majority of yellow counters, whereas Ling's results showed a higher proportion of red counters. These factors together suggest that Ling's results may be more representative of the overall bag contents.

A bag contains 150 counters - OCR - GCSE Maths - Question 19 - 2023 - Paper 3

Worked Solution & Example Answer:A bag contains 150 counters - OCR - GCSE Maths - Question 19 - 2023 - Paper 3

Use Riley's results to work out how many red counters are likely to be in the bag.

Use Ling's results to estimate the probability of choosing a red counter from the bag.

Explain why Ling's results are likely to give a better estimate of the probability of choosing a red counter from the bag than Riley's results.

Join the GCSE students using SimpleStudy...