Question

anthony spun a spinner a total of 100 times and recorded the number of times it had landed on red after different numbers of spins. his results are shown below.

a) work out the best estimate for the probability of the spinner landing on red. give your answer as a percentage.

b) anthony spins the spinner another 110 times. on how many of these 110 spins should he expect the spinner to land on red?

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$$\begin{tabular}{|c|c|c|c|c|} \\hline \\textbf{number of spins} & 10 & 20 & 50 & 100 \\\\ \\hline \\textbf{frequency of red} & 4 & 5 & 25 & 30 \\\\ \\hline \\end{tabular}$$

Explanation:

⚡ Using what you learned: experimental (empirical) probability

Step 1: Find the best estimate for the probability of landing on red

The best estimate for the probability of an event is the relative frequency calculated from the largest number of trials, as more trials lead to a more reliable estimate.

Using the data for \( 100 \) spins:

$$ \text{Number of spins} = 100 $$

$$ \text{Frequency of red} = 30 $$

Calculate the experimental probability:

$$ P(\text{red}) = \frac{30}{100} = 0.30 $$

Convert this to a percentage:

$$ 0.30 \times 100\% = 30\% $$

Step 2: Calculate the expected number of times landing on red

To find the expected frequency for another \( 110 \) spins, multiply the number of new trials by the estimated probability:

$$ \text{Expected value} = 110 \times 0.30 $$

$$ \text{Expected value} = 33 $$

Answer:

a) \( 30\% \)

b) \( 33 \)