Tag Archives: probability

## Probability

25 Feb

After we had been given back our assessments from last term and given instructions for how to review them we started looking at probability. The review process can be found here.

The first task was to carry out and True/False quiz on our phones (and some of Mr Rouse’s devices) using socrative, which is a student response website and app. The students have used this before…but obviously didn’t remember!

By creating a quiz and starting it from my account students can access it via their mobile devices using the room number unique to me. If anyone would like to use the Probability Misconceptions Quiz in their class you can add this SOC code in your socrative account SOC-693862. Mr Rouse

The live scores were displayed on the board as the students made their way through the quiz which involved the following questions:

A: FALSE

B: TRUE

C: FALSE

D: FALSE

E: FALSE

F: FALSE

G: FALSE

H: TRUE

I: FALSE

J: FALSE

The results can be viewed here with student names removed.

It shows that the next few lessons will need to focus on

• understanding of whether the outcomes are equally likely or not.
• being able to list outcomes systematically and accurately

The students are now starting to use www.rouseyear9.blogspot.co.uk to access information from our lessons.

Today’s blog was written by Mr Rouse

## Probability Tree Diagrams

24 Jan

In today’s lesson we are looking to move onto level 6 and 7 probability by using tree diagrams to find the probability for two events. To introduce the topic Mr Rouse used two pieces of string folded over and held in his hand. This is similar to a Russian tradition for deciding whether a couple should Marry (works better in a mixed school!) “The Couple” tie the ends together, what are the possible outcomes? One outcome means they should be married, one means they shouldn’t. Is this where tying the knot comes from? We then worked through an example of using a tree diagram for a situation where we had the probabilities of 1. Jay riding his bike to school, which was 1/3 2. Mr Rouse taking public transport to school, which was 2/3 The tree diagram is shown below:

We discussed that in probability if the situation you are looking at can be described by saying

“what is the probability of _____ and ______” then you multiply the probabilities

or

“what is the probability of ______ or _______” then you add the probabilities

In Probability

AND = x

OR = +

We are going to try and apply these ideas to these situations next time:

## Experimental Probability versus Theoretical Probability

16 Jan

Today we started by writing in our books a number between 1 and 12 for a horse race. For the horse to move you had to roll a dice twice and add the scores to equal one of the numbers. Number 7 was winning the majority of the race with 5 and 6 hot on their tales, but in the end 5 won!

To find out the probability that each horse would win, we drew a Sample Space Diagram to help us. With the Sample Space Diagram we put the numbers on the outside. On the inside 7 had the most numbers. Underneath the diagram we put some questions down which were referring to why did 5 win if there were more 7’s in the graph than fives?

Then on the board we put theoretical probabilities of outcomes when you add score on 2 dice, also we put experimental of outcome when we rolled two dice and added the scores.

Next race:

At the start of the new race the horses were based on the difference between the two dice. We had to draw a sample space diagram of the outcomes of this before we chose our horse for the race. The numbers only went up to 5.

Here is the result and the theory next to each other.

Today’s blog was written by Milo and additions by Mr Rouse

## Probability

10 Jan

Today’s starter was simplifying fractions  for example 7/14  would be 1/2 .

Our next activity was a range of probability questions ranging from Level 6 to L7.

Some of the answers to these questions are:

1.3/4                                                                                                      7.2/3

2.4/7                                                                                                      8.3/4

3.4/11                                                                                                     9.3/8

4. smallest probability 0 – highest probability 1                   10.1

5.2/3                                                                                                        11.3/4

6.2/3                                                                                                         12.1/3

The students made good progress to level 6. After some input on higher levels they will try to push on to level 6 and 7.

Today’s blog was written by Mason

## Probability Misconceptions

7 Jan

In Today’s lesson the students were given a true/false quiz using socrative.com. Mr Rouse had entered a set of 10 questions based on probability which the students could access via mobile technology.

The results were displayed on the screen and showed that the students had some misunderstanding on some of the concepts underlying probability. The student’s scores out of 10 are shown below.

 6 3 3 2 7 4 7 5 6 4 5 7 6 5 2

The probability questions are shown below (These are taken from the standards unit for Mathematics), E and H were answered incorrectly by most students:

In pairs the students were asked to write explanations for each question after having seen the answers and having time to discuss them. Here are their explanations:

A:

A is false because it has an equal chance of being either, but it could be 1,2,3 or 5 as well as 6 and 4

B:

B is true because there are twice as many combinations of equaling three than two on a two dice.

C:

C is false because there are 49 numbers in the lottery there is a 1 in 49 chance that you would get the number correct. The six numbers all have an equal chance.

D:

D is false because there are two ways of getting one head making this outcome more likely.

E:

E is false because the teams are not even and it would be more likely that the bigger team would win.

F:

G:

G is false because it is a 50/50 chance

H:

H is true because one is definitely certain whatever happens. Also it is in a week so its most likely to happen with ten children

I:

After some discussion of the biology of the situation… If you have four girls its still a 50% chance to have a girl

J:

The students struggled to suitably explain this (and will without level 8 probability or higher) In discussion we decided that there was not an equal chance of getting three heads as there would be for any other outcome.

Summary:

The key idea seems to be about knowing when there is an equal chance of each of the outcomes happening or whether there is not.