Flippin' Discs

Tamsin from Ringmer Primary School correctly states that

With 2 discs you win approximately half the time.

Congratulations to Thomas from Dalton School in New York for his correct solution:

The probability of obtaining the same colour with two discs is 1/2 because there are two ways of obtaining this result (red-red, green-green) and there are four combinations in total (red-red, green-green, red-green, and green-red). Hence, the probability is 2/4, which simplifies to 1/2.

For three discs, the probability is 1/4 using the same logic - there are two ways of obtaining the same colour and eight combinations in total (2 $\times$2 $\times$2, or 2$^3$).

For four discs, the probability is 1/8 because there are two ways of obtaining the same colour and sixteen combinations in total (2 $\times$2 $\times$2 $\times$2, or 2$^4$).

The general formula for the probability of flipping n discs and obtaining the same colour is:

$2/ 2^n$ or $1/ 2^{(n-1)}$.

Emma from St. Paul's Girls' School also found that

The probability of winning for n discs = 1/(2 to the power n-1)

Adan from Bancroft's uses Pascal's Triangle to help him determine the total number of possible combinations:

Firstly you must match the number of discs with the line of that number but one higher.