Question

1. communication the table shows the results for a mystery spinner.

colour	favourable outcomes, n(a)
green	2
purple	3
blue	1

a) determine the experimental probability of the spinner landing on each colour.
b) draw what the spinner could look like, based on the given data.
c) could the real spinner look different? explain.

Explanation:

Part (a)

Step 1: Calculate Total Outcomes

First, find the total number of trials by summing the favourable outcomes for all colours.
Total outcomes, \( n(S) = 6 + 2 + 3 + 1 = 12 \)

Step 2: Experimental Probability for Yellow

Experimental probability \( P(\text{Yellow}) = \frac{n(\text{Yellow})}{n(S)} = \frac{6}{12} = \frac{1}{2} \)

Step 3: Experimental Probability for Green

\( P(\text{Green}) = \frac{n(\text{Green})}{n(S)} = \frac{2}{12} = \frac{1}{6} \)

Step 4: Experimental Probability for Purple

\( P(\text{Purple}) = \frac{n(\text{Purple})}{n(S)} = \frac{3}{12} = \frac{1}{4} \)

Step 5: Experimental Probability for Blue

\( P(\text{Blue}) = \frac{n(\text{Blue})}{n(S)} = \frac{1}{12} \)

To draw the spinner, divide the circle into 12 equal parts (since total outcomes are 12). Then:

• Yellow: \( \frac{1}{2} \times 12 = 6 \) parts
• Green: \( \frac{1}{6} \times 12 = 2 \) parts
• Purple: \( \frac{1}{4} \times 12 = 3 \) parts
• Blue: \( \frac{1}{12} \times 12 = 1 \) part

Color 6 parts yellow, 2 parts green, 3 parts purple, and 1 part blue. The spinner can be a circle with these sections proportionally sized.

Yes, the real spinner could look different. Experimental probability is based on trials, and the actual spinner's area for each color (theoretical probability) might not match the experimental one exactly. For example, the spinner could have non - equal - sized sectors, but due to randomness in spinning, the experimental results (favourable outcomes) gave the probabilities calculated. The real spinner's color areas could be in different proportions, but with enough spins, the experimental probability should approach the theoretical probability.

Answer:

• Yellow: \( \boldsymbol{\frac{1}{2}} \)
• Green: \( \boldsymbol{\frac{1}{6}} \)
• Purple: \( \boldsymbol{\frac{1}{4}} \)
• Blue: \( \boldsymbol{\frac{1}{12}} \)

Part (b)