KS3 Maths - Probability Question

[chlorinata]

DS has described this problem from memory, but the answer we get doesn't tally with the answer he remembers from school, so I just want some reassurance that we've done it right:

Q: A child spins two spinners labelled 1-5. What is the probability of the two numbers adding together to make a number less than 7.

His Method: Make a matrix of all the possible values of the spinners (with the values they add up to in brackets) :

1    2    3    4    5

1 (2) (3) (4) (5) (6)
2 (3) (4) (5) (6) (7)
3 (4) (5) (6) (7) (8)
4 (5) (6) (7) (8) (9)
5 (6) (7) (8) (9) (10)

There are 25 possible outcome, and the number of outcomes

No double counting.

His method sounds right.

Assuming equal spacing on the spinners/fair spinners

He's absolutely right as is Pickle.
He has used the correct method to do it too.
(maths degree & child in y9)

(Sorry if ^^ sounds a bit pompous but I get a bit fed up on BODMAS threads in Chat with people ignoring the 5 of us with maths degrees in favour of completely wrong suggestions from others, even when given a clear explanation in the first 5 responses).

Might be worth to explain to him why double counting is not required so he get a deeper understanding.

To get 1+1, the first choice has to be a 1 and second choice has to be 1 as well, so there's only one option for each choice.

However, to get 2+1 or 1+2, the first choice can be 1 or 2 and the second choice can be the one remained (i.e. if first choice is 1, second choice has to be 2; if first choice is 2 second has to be 1), therefore there are two options for first choice and one option for second choice. Since probability of picking each number is the same, probability of get 1,2 or 2,1 has to be double that of getting 1,1, therefore no double counting.