Handling Data - Probability 2

Probability is all about how likely it is for something to happen. Probability is the likelihood or chance of an event happening.

Lets take this a step further - What if we had two dice and wanted to know

What is the probability of throwing a total of 1?

It is impossible because by throwing two dice, the lowest score we could ever achieve would be 2 - a '1' on the first dice and a '1' on second dice. So the probability is 0

What is the probability of throwing a total of 12?

We would have to throw a 6 with both dice. How many outcomes are there?

Lets label the two dice, dice A and dice B. Dice A could land on 1,2,3,4,5 or 6, and
If dice A lands on 1, what outcomes are there for dice B? It could land on 1,2,3,4,5 or 6
If dice A lands on 2, what outcomes are there for dice B? It could land on 1,2,3,4,5 or 6
If dice A lands on 3, what outcomes are there for dice B? It could land on 1,2,3,4,5 or 6
If dice A lands on 4, what outcomes are there for dice B? It could land on 1,2,3,4,5 or 6
If dice A lands on 5, what outcomes are there for dice B? It could land on 1,2,3,4,5 or 6
If dice A lands on 6, what outcomes are there for dice B? It could land on 1,2,3,4,5 or 6

So there are 6 different combinations of 6 .... 6 outcomes for each position that dice A could land on ....... 6 x 6 = 36 possible outcomes.

This is getting complicated - lets make it easier to understand with a table.

Data

This table shows all the possible totals by adding all the possible combinations from Dice A and Dice B. As we deduced before, there are 36 different combinations.

So by looking at the table there are 36 possible outcomes, how many of those outcomes result in a twelve, just one - 1 out of 36.

As a fraction 1/36 ... As a decimal 1 ÷ 36 = 0.028 ... As a percentage 0.028 x 100 = 2.8%

What is the probability of throwing a total of 2?

by looking at the table there are 36 possible outcomes, how many of those outcomes result in a two, just one - 1 out of 36.

As a fraction 1/36 ... As a decimal 1 ÷ 36 = 0.028 ... As a percentage 0.028 x 100 = 2.8%

What is the probability of throwing a total of 3?

by looking at the table there are 36 possible outcomes, how many of those outcomes result in a three, just two - 2 out of 36.

As a fraction 2/36 which can be simplified to 1/18 ... As a decimal 1 ÷ 18 = 0.055
... As a percentage 0.055 x 100 = 5.5%

What is the probability of throwing a total of 7?

by looking at the table there are 36 possible outcomes, how many of those outcomes result in a seven, there are six - 6 out of 36.

As a fraction 6/36 which can be simplified to 1/6 ... As a decimal 1 ÷ 6 = 0.166
... As a percentage 0.166 x 100 = 16.6%

Work out the probability of throwing the other numbers.

By using a table, we have made it easier to understand the data, but we are still doing the same thing - working out all the possible outcomes.

 

Try this Probability Quiz from BBC Bitesize

Practice with this interactive activity

Play in Full Screen

The question is .... What is the probability of passing the 11 Plus?

Handling Data - Probability 1  Maths Index  Maths Index








CAT4 / 12 Pus papers