A bag contains 150 counters. The counters are either red or yellow. Riley picks a counter from the bag, records its colour, and replaces it. He does this nine times. Here are Riley's results. Red Yellow Use Riley's results to work out how many red counters are likely to be in the bag. (a) ................................................. red counters (b) Ling uses the same bag of counters and picks the counters in the same way. Here are Ling's results. Red Yellow Use Ling's 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 3 - 2023 - Paper 6

Question 3

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

Worked Solution & Example Answer:A bag contains 150 counters - OCR - GCSE Maths - Question 3 - 2023 - Paper 6

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, with 3 being red.
To estimate the total number of red counters in the bag, we can use the ratio of red to total counters.

Let the number of red counters be denoted as $R$ .
Using the proportion, we have:
$\frac{R}{150} = \frac{3}{9}$
Solving for $R$ :
$R = 150 \times \frac{3}{9} = 150 \times \frac{1}{3} = 50$
Thus, there are likely 50 red counters in the bag.

Step 2

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.

99%

104 rated

Answer

Ling's results show 5 red counters out of 9 total picks.
Thus, the estimated probability $P$ of picking a red counter is:
$P = \frac{\text{Number of red counters}}{\text{Total counters picked}} = \frac{5}{9}$
Therefore, the probability of choosing a red counter from the bag is $\frac{5}{9}$ .

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 are likely to provide a better estimate for several reasons.
Firstly, Ling conducted more trials (9 comparisons) compared to Riley, which reduces the impact of random chance and makes her estimate more reliable.
Secondly, more data points generally lead to a more accurate reflection of the actual population, as it helps account for variability, thereby giving a fuller picture of the counter distribution in the bag.
Consequently, Ling's larger sample size likely results in a better approximation of the actual ratio of red to yellow counters.

A bag contains 150 counters - OCR - GCSE Maths - Question 3 - 2023 - Paper 6

Worked Solution & Example Answer:A bag contains 150 counters - OCR - GCSE Maths - Question 3 - 2023 - Paper 6

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. Give your answer as a fraction in its simplest form.

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...