Chapter 23: Review

Return to the chapter problem

For a spinner with equal-sized red and blue regions, each spin has probability $\frac12$ of landing on red. Over many spins, the relative frequency should be near $\frac12$, although a short run can differ.

If the spinner is spun 80 times and lands on red 47 times, the relative frequency is $\frac{47}{80}=0.5875$. This result does not prove that the spinner is unfair. More trials may move the estimate nearer or further from $\frac12$.

Mixed practice

Choose a method before working. For each question, state which method applies and why.

1. A fair six-sided die is rolled. Find the probability of rolling a factor of 6. Give your answer as a fraction.
2. A coin lands heads 38 times in 80 tosses. Find the relative frequency of heads.
3. A bag has 3 red and 2 blue counters. One counter is chosen and replaced, then another is chosen. Find the probability of two reds.
4. From 40 students, 22 study French, 18 study Spanish and 7 study both. Find how many study neither language.
5. In a group of 30, 12 wear glasses. Of those wearing glasses, 8 travel by bus. Find the probability that a student travels by bus given that they wear glasses.
6. A temperature changes from $-4^\circ\text{C}$ to $3^\circ\text{C}$. Work out the increase. Which earlier number method applies?
7. A recipe uses 250 g of flour for 10 biscuits. Work out the flour needed for 16 biscuits. Explain which method applies.

Reflect

Write one probability idea you can now explain. Name a question where you would use a sample space, tree diagram, Venn diagram or conditional probability, and give a reason for your choice.