Chance and probability · Usually met around P3
Listing all the outcomes
Fix the first, then pair it with each of the second.
How to do it
Method
Fix the first, then pair it with each of the second
$1 and $2 coins: HH, HT, TH, TT
Another way
Draw a table
H, T down the side; red, blue, yellow on top: 6 boxes
In full
List the outcomes in order, so none is repeated and none is missed. A coin has 2 outcomes, heads (H) and tails (T). When two things happen together, fix the first one's outcome and pair it with each of the second's in turn: tossing a $1 coin and a $2 coin gives HH, HT, TH, TT, 4 in all (HT and TH are different). Or draw a table: the first thing's outcomes down the side, the second's along the top, and each box is one outcome. Some events can't happen together: on one roll of a dice, “rolling a 2” and “rolling an odd number” never both happen.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Roll a dice once. “Rolling a 1” and “rolling a number greater than 2” can happen at the same time.
True or false?
Show the answer and working
Answer: False
With one roll, both happen only if the 1 rolled is greater than 2.
Example 2
Spinner A shows 1 to 2 and spinner B shows 1 to 4. Spin each once and add the two numbers. There are □ outcomes in all, and □ of them give a total of 4.
Fill in each box
Show the answer and working
Answer: 8，2
Draw a table, A's 2 numbers down the side and B's 4 along the top: 8 boxes, and 2 of them total 4.
Example 3
Make two-digit numbers with the cards 3, 7 and 0, using two cards each time. How many different two-digit numbers can be made?
Show the answer and working
Answer: 4
Fix the tens digit, then pair it with each ones digit in turn; 0 can't be the tens digit. 4 in all.
Practise it in the game →Chance and probability · Free to start, unlimited questions, no download