A Family A had five children – Patricia – Mary – Susan – Helen – Kathleen – What were the chances of the next baby being a boy?

Spinning coins Notesheet Lesson 17 Probability

Activity 1 Heads and tails We can use coins to model probability or chance. When you spin a coin how likely is it that you will get a long run of heads?

Do you think it is easier or harder to get three heads in a row than to get ten heads in a row? Why do you think that?

Let us test out your ideas. Spin one coin fifty times and record if it lands heads (H) or tails (T) in the Table A. Or Take 10 coins lay them in a line and spin each one. Record H or T in Table A :-repeat five times.

Table A Runs of heads

Activity 2 The frequency of runs Let us look at runs of heads in your group’s fifty throws (Table A). Use a coloured pen to highlight all the single heads, a different colour for a run of two heads, a different colour to mark runs of three heads, another colour for four heads etc. Put the number of each type of run (1s, 2s, 3s, 4s etc.) into the frequency Table B.

Table B Frequency

1 To the nearest whole number, how many times did you get one head on its own compared with runs of two heads? 2 To the nearest whole number, how many times more runs of two heads are there than runs of three heads? 3 Can you see any pattern in your frequency table?

Now add your group’s data to the class results. Link to excell work book Looking at the class results, discuss these questions in your group:

4 Is there a pattern in the runs of heads? 5 To the nearest whole number, how many times more runs of two heads are there than runs of three heads? 6 Suppose you throw two heads in a row. On the next throw, what do you think are the chances of getting a head? 7 Does the answer to Question 6 explain your answer to Question 5? Link if you skip activity 3.

Activity 3 Small samples What do you notice about the number of heads in a sample of ten compared with a sample of fifty coin throws? From Table A, count the number of heads in the first set of ten throws, then in the second set of ten throws, then in the third set etc. Complete Table C

Did you get exactly five heads in any of the sets of ten throws? What was the largest number of heads in any set of throws? What was the smallest number of heads in any of your sets of throws?

Did you get exactly five heads in any of the sets of ten throws? What was the largest number of heads in any set of throws? What was the smallest number of heads in any of your sets of throws?

A set of ten throws is a sample of the possible ratio of heads to tails. What are the chances of a head being thrown? What are the chances of a tail being thrown? Why?

How many times do you think you would have to throw a coin to get equal numbers of heads and tails in the whole sample? Take a guess. Does a sample of ten throws tell us much about the ratio of heads to tails? How many sets would you want to look at to give you a big enough sample for you to look for a pattern, a ratio? Take a guess.

Girl or a boy? People say that each time a baby is conceived it has an equal chance of being a girl or a boy. You could not look at every single birth record in the country to find the ratio of boy babies to girl babies. It would take you too long.

How many babies would you have to count in the birth records of a hospital before you could be sure that there is an equal chance of a baby being born a boy or a girl? Take a guess.

We can find out how good your guess is. Look at the plotted graph for all the results of heads in sets of ten throws from all the groups in your class.

What happens to the line on the graph? (link if you have done activity 3) What happens to the proportion of heads as the sample gets larger and larger? How large (how many throws of the coin) before the sample shows the proportion of heads is 0.5?

In what other ways can you say the same thing? So how many records would you look at to get a good idea of the real proportions in the whole population of babies?