InvestigationReasoning Flipping heads with a coin Experimental probability 1 What is the theoretical probability of flipping Heads with a fair coin? Write your answer as a decimal. 2 a Flip a coin 20 times and record the results in a frequency table. b Calculate the experimental probability of Heads. Write your answer as a decimal. 3 a Combine your data with a classmate. b Calculate the experimental probability of Heads based on 40 flips. 4 Combine the data of more classmates, one at a time. Calculate the experimental probability of Heads based on 60, 80, 120 ... flips. 5 Plot the results on a graph like the one shown on the right. 1 0.8 0.6 0.4 0.2 0 0 20 40 60 80 100120140160 Number of flips 6 What do you notice about the experimental probabilities as the number of trials increases? 6 a An ordinary 6-sided dice is rolled 30 times. How many times do you expect a 5? b An ordinary pack of playing cards is shuffled and the top card turned over 100 times. How many times do you expect the top card to be a Spade? c A bag contains 3 red and 2 blue counters. A counter is picked at random and then replaced, 40 times. How many red counters do you expect? 7 Reasoning In a fantasy game, players use a spinner to see which creature they have to fight. a What is the theoretical probability of landing on Vampire if the spinner is fair? b How many times would you expect the spinner to land on each creature in 100 spins? These are the results for 100 spins. Creature Frequency Zombie Vampire Ghost Werewolf Vampire Werewolf Ghost Zombie 22 27 25 26 Key point Theoretical probability can be used to calculate the frequencies you would expect in an experiment. Explore 8 Explore How many times do you have to flip a coin to be confident that it is a fair coin? Is it easier to explore this question now you have completed the lesson? What further information do you need to be able to answer this? Reflect c Kuni says that the spinner is fair. Do you agree? What could she do to be more confident that the spinner is fair? 9 Reflect In this lesson you learned about experimental probability. In lesson 8.3 you learned about relative frequency. a In what way are experimental probability and relative frequency the same? b Describe a situation where you might use experimental probability to describe an event. Describe a situation where you might use relative frequency to describe an event. 183 Delta 2, Section 8.4 Topic links: Adding fractions, Graphs