Question

emmie and delilah each spun the same spinner a number of times and recorded how many times it landed on 2

a) they each used their own results to work out the estimated probability of the spinner landing on 2. which person had the better estimate for the probability?

b) by combining their results, work out the estimated probability of the spinner landing on 2. give your answer as a decimal.

c) will the combined results give a better or worse estimate than using only one persons results? write a sentence to explain your answer.

Explanation:

⚡ Using what you learned: experimental (empirical) probability

Step 1: Analyze part (a)

The reliability of an experimental probability estimate increases as the number of trials increases.

• Emmie's total number of spins: \(20\)
• Delilah's total number of spins: \(30\)

Since Delilah spun the spinner more times, her results provide a larger sample size. Therefore, Delilah had the better estimate.

Step 2: Calculate part (b)

To find the combined estimated probability, sum the successful outcomes and divide by the sum of the total trials:

$$ \text{Total successful outcomes (landing on 2)} = 18 + 17 = 35 $$

$$ \text{Total number of spins} = 20 + 30 = 50 $$

$$ \text{Combined estimated probability} = \frac{35}{50} = \frac{70}{100} = 0.7 $$

Step 3: Analyze part (c)

Combining the results increases the overall sample size to \(50\) trials. A larger number of trials reduces the impact of random chance, making the experimental probability closer to the theoretical probability. Therefore, the combined results will give a better estimate.

Answer:

a) Delilah had the better estimate because she carried out more spins (a larger number of trials).

b) \(0.7\)

c) Better estimate. Combining the results increases the total number of trials, which makes the estimated probability more reliable and closer to the true probability.